The length of a body is measured as 3.51 m, if the accuracy is 0.01 mm, then the percentage error in the measurement is

(a)

35.1%

(b)

1%

(c)

0.28%

(d)

0.035%

Astromical Scale is dealt with the _________ Physics

(a)

Mesoscopic

(b)

Microscopic

(c)

Macroscopic

(d)

None

Which of the following statement is wrong?

(a)

one fenni = 10¹⁵ m

(b)

All non-zero digits are significant.

(c)

1 AU = 1.496 \(\times\)10¹¹m

(d)

Speed is a derived unit

Unit of reduction factor is

(a)

ampere

(b)

ohm

(c)

tesla

(d)

weber

1 Wb/\({ m }^{ 2 }\) is eqaul to  

(a)

\({ 10 }^{ 4 }\) G

(b)

\({ 10 }^{ 2 }\) G

(c)

\({ 10 }^{ -2 }\) G

(d)

\({ 10 }^{ -4 }\) G

A student measures the thickness of a human hair by looking at it through a microscope of magnification 100. He makes 20 observations and finds that the average width of the hair is 3.5 mm. What is the estimate on the thickness of the hair?

(a)

0.0035 mm

(b)

0.035 mm

(c)

0.01 m

(d)

0.7 mm

The dimensional representation of specific resistance in terms of charge Q is

(a)

\(\left[ M{ L }^{ 3 }{ T }^{ -1 }{ Q }^{ -2 } \right] \)

(b)

\(\left[ M{ L }^{ 2}{ T }^{ -2 }{ Q }^{ 2 } \right] \)

(c)

\(\left[ M{ L }^{ }{ T }^{ -2 }{ Q }^{ -1 } \right] \)

(d)

\(\left[ M{ L }^{ 2 }{ T }^{ -2}{ Q }^{ -1 } \right] \)

The SI unit of thermal conductivity is

(a)

\(Js{ m }^{ -1 }{ K }^{ -1 }\)

(b)

\({ W}^{ -1 }{ m }^{ -1 }{ K }^{ -1 }\)

(c)

\({ W}^{ }{ m }^{ -1 }{ K }^{ -1 }\)

(d)

\({ W}^{ }{ m }^{ -2 }{ K }^{ -1 }\)

A capillary tube is attached horizontally to a constant heat arrangement. If the radius of the capillary tube is increased by 10%, then the rate of flow of liquid will change nearly by

(a)

+10%

(b)

+46%

(c)

-10%

(d)

-40%

The position of the particle moving along Y-axis is given as y = At² - Bt³, where y is measured in metre and t in second. Then, the dimensions of B are

(a)

[LT^-2]

(b)

[LT^-1] 

(c)

[LT^-3]

(d)

[MLT^-2]

If energy (E), velocity (v) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be

(a)

[Ev^-2T^-1]

(b)

[Ev^-1T^-2]

(c)

[Ev^-2T^-2]

(d)

[E^-2v^-1T^-3]

The dimensional formula of magnetic flux is

(a)

\(\left[ ML^{ 2 }T^{ -2 }A^{ -1 } \right] \)

(b)

\(\left[ ML^{ 2 }T^{ -3 }A^{ -1 } \right] \)

(c)

\(\left[ M^{ -1 }L^{ -2 }T^{ 2 }A \right] \)

(d)

\(\left[ ML^{ 3 }T^{ -2 }A^{ -1 } \right] \)

One picofarad is equal to ___________farad.

(a)

10^-18

(b)

10^-12

(c)

10^-6

(d)

10^-24

The angle subtended by a coin of radius 1 em held at a distance of 80 em from your eyes is ______________.

(a)

1.43⁰

(b)

0.72⁰

(c)

0.0125⁰

(d)

0.025⁰

The frequency of vibration f of a mass m suspended from a spring of spnng constant k is given by a relationf = am^xk^y, when a is a dimensionaless constant. The values of x and y are ______________.

(a)

\(x=\frac{1}{2},y=\frac{1}{2}\)

(b)

\(x=-\frac{1}{2},y=-\frac{1}{2}\)

(c)

\(x=\frac{1}{2},y=-\frac{1}{2}\)

(d)

\(x=-\frac{1}{2},y=\frac{1}{2}\)

One parsec is_______________.

(a)

3.153\(\times\)10⁷ m

(b)

3.26\(\times\)10¹⁵ m

(c)

30.84\(\times\)10¹⁵ m

(d)

9.46\(\times\)10¹⁵ m

The force F is given by F = at + bt² where t is time. The dimensions of 'a' and 'b' respectively are _____________.

(a)

[M LT^-3] and [MLT^-4]

(b)

[M LT^-4] and [MLT^-3]

(c)

[M LT^-1] and [MLT^-2]

(d)

[M LT^-2] and [MLT^-0]

Imperfections in experimental procedure gives______errors.

(a)

random

(b)

gross

(c)

systematic

(d)

personal

The unit of moment of force_______

(a)

Nm²

(b)

Nm

(c)

N

(d)

NJ rad

Relative error can also be called as____________.

(a)

fractional error

(b)

absolute error

(c)

percentage error

(d)

systematic error

A men wants to reach point B on the opposite bank of a river flowing at a speed as shown in figure.What minimum speed relative to water should the man have ,so that he can reach point B?

(a)

\(u\sqrt { 2 } \)

(b)

\( { u }/{ \sqrt { 2 } } \)

(c)

\(2u\)

(d)

\({ u }/{ 2 } \)

\(\int^{2}_{1}\) \(dx\over x^{2}\) is

(a)

\(1\over2\)

(b)

\(-{1\over2}\)

(c)

\({1\over4}\)

(d)

\(-{1\over4}\)

For the resultance of two vectors to be maximum what must be the angle between them

(a)

0^o

(b)

60^o

(c)

90^o

(d)

180^o

At the top of the trajectory of a particle, the acceleration is

(a)

maximum

(b)

minimum

(c)

zero

(d)

g

A ball is projected upwards from the top of a tower with velocity 50 ms^-1 making an angle of 30° with the horizontal. If the height of the tower is 70m, after what time from the instant of throwing, will the ball reach the ground ? (g = 10ms^-2 )

(a)

2 s

(b)

5 s

(c)

7 s

(d)

9 s

A ball is rolled off the edge of a horizontal table at a speed of 4 ms^-1. It hits the ground after 0.4 s. Which statement given below is true.

(a)

It hits the ground at a horizontal distance 1.6 m from the edge of the table

(b)

The speed with which it hits the ground is 4.0 ms¹

(c)

Height of the table 1m

(d)

It hits the ground at an angle of 60° to the horizontal

Balls A and B are thrown from two points lying on the same horizontal plane separated by a distance 120 m. Which of the following statement (s)is/are correct?

(a)

The two balls can never meet

(b)

The balls can meet if the ball B is thrown 1 slater

(c)

The two balls meet at a height of 45 m

(d)

None of the above

If \(\bar A\)and \(\bar B\) are two vectors, \(\bar A.\bar B=\bar A\times\bar B\) then resultant vector is ____________.

(a)

A+B

(b)

A-B

(c)

\(\sqrt {A^2+B^2}\)

(d)

\(\sqrt {A^2+B^2+\sqrt{2}AB}\)

If x = a cost is the displacement in time t then, acceleration is ____________

(a)

a cost

(b)

-a cost

(c)

a sint

(d)

-a sint

A particle moves along a straight line such that its displacement at any time t is given by s = (t³ - 6t² + 3t + 4) metres. The velocity when the acceleration is zero is _____________.

(a)

3 m/s

(b)

42 m/s

(c)

-9 m/s

(d)

-15 m/s

If \(\vec R=\vec P+\vec Q\), then which of the following is true?

(a)

P>Q

(b)

Q>P

(c)

P=Q

(d)

R>P, Q

The scalar product of two vectors will be maximum when \(\theta\) is equal to ______________.

(a)

0^o

(b)

90^o

(c)

180^o

(d)

270^o

The momentum of a particle is \(\vec P=\cos\theta\hat i+\sin\theta\hat j\) . The angle between momentum and the force acting on a body is ______________.

(a)

0^o

(b)

45^o

(c)

90^o

(d)

180^o

In non-uniform circular motion, the resultant acceleration is given by ______________.

(a)

\(a_R=\sqrt{a_t^2-(\frac{V^2}{r})^2}\)

(b)

\(a_R=\sqrt{a_t^2+(\frac{V^2}{r})^2}\)

(c)

\(a_R=\sqrt{a_t^2-(\frac{r}{V^2})^2}\)

(d)

\(a_R=\sqrt{a_t^2+(\frac{r}{V^2})^2}\)

A car moves from X to Y with a uniform speed V_n and returns to Y with a uniform speed V_d The average speed for this round trip is _____________.

(a)

\(\sqrt{V_uV_d}\)

(b)

\(\frac{V_uV_d}{V_d+V_u}\)

(c)

\(\frac{V_u+V_d}{2}\)

(d)

\(\frac{2V_dV_u}{V_d+V_u}\)

Three forces F₂, F₂ & F₃ are acting on a particle of mass m such that F₂ & F₃ are mutually perpendicular, then the particle remains stationary. If the force F₁ is now removed, then the acceleration of the particle is _____________.

(a)

\(\frac { { F }_{ 1 } }{ m } \)

(b)

\(\frac { { F }_{ 2 }{ F }_{ 3 } }{ mF } \)

(c)

\(\frac { { F }_{ 2 }-{ F }_{ 3 } }{ m } \)

(d)

\(\frac { { F }_{ 2 } }{ m } \)

A block is kept on a frictionless inclined surface with angle of inclination ∝, The incline is given an acceleration a to keep the block stationary. Then a is equal to _____________.

(a)

g cosec ∝

(b)

g

(c)

\(\frac { g }{ tan\ \alpha } \)

(d)

g tan ∝

Three blocks of masses 2 kg, 3 kg and 5 kg are connected to each other with light string & then placed on a frictionless surface. The system is pulled by a force F = 10N, then tension T₁ is ______________.
 

(a)

1N

(b)

8N

(c)

5N

(d)

10N

The mass m is placed on a body of mass M. There is no friction. The force F is applied on M and it moves with acceleration a. Then , the net force on the top body is

(a)

F

(b)

ma

(c)

F - ma

(d)

None of these

Two rods X and Y are attached to a weight of mass M as shown in figure , then

(a)

both X and Y experience compression

(b)

both X and Y experience extension

(c)

Y experiences extension and X compression

(d)

Y experiences compression and X extension

A block of mass m is in contact with the cart C as shown in the figure. The coefficient of static friction between the block and the cart is \(\mu\) . The acceleration \(\alpha\)  of the cart that will prevent the block from failling statistics.

(a)

\(\alpha =\frac { mg }{ \mu  } \)

(b)

\(\alpha =\frac { g }{ \mu m } \)

(c)

\(\alpha \ge \frac { g }{ \mu  } \)

(d)

\(\alpha >\frac { g }{ \mu  } \)

A balloon of weight w is falling vertically downward with a constant acceleration

(a)

w

(b)

\(w\left( 1+\frac { a }{ g } \right) \)

(c)

\(w\left( 1-\frac { a }{ g } \right) \)

(d)

\(w\frac { a }{ g } \)

A 100 N force acts horizontally on a block of mass 10 kg placed on a horizontal rough table of coefficient of friction \(\mu\) = 0.5. If g at the place is 10 ms² , the acceleration of the block is

(a)

zero

(b)

10 m/s²

(c)

5 m/s²

(d)

5.2 m/s²

Two particles of equal mass are connected to a rope AB of negligible mass, such that one is at end A and the other dividing the length of the rope in the ratio 1: 2 from A. The rope is rotated about end B in a horizontal plane. Ratio of the tensions in the smaller part to the other is (ignore effect of gravity)

(a)

4:3

(b)

1:4

(c)

1:2

(d)

1:3

A bullet moving with a velocity of \(30\sqrt { 2 } { ms }^{ -1 }\) is fired into a fixed target. It penetrated into the target to the extent of s metres. If the same bullet is fired into a target of thickness \(\frac { s }{ 2 } \) metres and of the same material with the same velocity, then the bullet comes out of the target with velocity

(a)

20 ms^-1

(b)

30 ms^-1

(c)

\(20\sqrt { 2 } { ms }^{ -1 }\)

(d)

\(10\sqrt { 2 } { ms }^{ -1 }\)

A marble block of mass 2 kg lying on ice when given a velocity of 6 ms^-1 is stopped by friction is 10 s. Then the coefficient of friction is

(a)

0.01

(b)

0.02

(c)

0.03

(d)

0.06

A particle moves in a circle of radius 5 cm with constant speed and time period \(0.2 \pi\) s . The acceleration of the particle is 

(a)

25 m/s²

(b)

36 m/s²

(c)

5 m/s²

(d)

 15 m/s²

The distance of a particle moving on a circle of radius 12m measured from a fixed point on the circle and measured along the circle is given by s = 2t³ (in meters). The ratio of its tangential to centripetal acceleration at t = 2s is

(a)

1:1

(b)

1:2

(c)

2:1

(d)

3:1

Second law of Newton gives the ______ definition of force.

(a)

fundamental

(b)

quantitative

(c)

dimensional

(d)

both (b) and (c)

Newton's second and third laws of motion lead to the conservation of ______________.

(a)

linear momentum

(b)

angular momentum

(c)

potential energy

(d)

kinetic energy

Change in momentum of a body is ________________.

(a)

force

(b)

acceleration

(c)

work

(d)

impulse

According to the conservation of linear momentum ________________.

(a)

momentum before impact = momentum after impact

(b)

momentum before impact > momentum after impact

(c)

momemtum before impact < momentum after impact

(d)

momentum before impact is inversely proportional to momentum after impact

One end of string of length l is connected to a particle of mass 'm' and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed 'v', the net force on the particle (directed towards centre) will be (T represents the tension in the, string) ______________.

(a)

\(T+\frac { mv^{ 2 } }{ l } \)

(b)

\(T-\frac { mv^{ 2 } }{ l } \).

(c)

zero

(d)

T

A person of mass 60 kg is inside a lift of mass 940 kg and presses the button on control panel. The lift starts moving upwards with an acceleration 1.0  m/s^-2. If g = 10 ms^-2, the tension in the supporting cable is _____________.

(a)

8600 N

(b)

9680 N

(c)

11000 N

(d)

1200 N

On the horizontal surface of a truck a block of mass 1 kg is placed (m = 0.6) and truck is moving with acceleration 5 m/sec² then the frictional force on the block will be ______________.

(a)

5 N

(b)

6 N

(c)

5.88 N

(d)

8 N

A body is falling from a height h. After it has fallen a height \(\frac{h}{2}\) it will possess _______________

(a)

only Potential Energy

(b)

only Kinetic Energy

(c)

half potential and half kinetic energy

(d)

more kinetic and less potential energy

A particle of mass m₁ is moving with a velocity v, and another of mass m₂ is moving with velocity v₂ Both of them have the some momentum but their kinetic energies are E₁ and E₂ respectively. If =m₁ > m₂ the ______________.

(a)

E₁2

(b)

\(\frac{E_1}{E_2}=\frac{m_1}{m_2}\)

(c)

E₁>E₂

(d)

E₁=E₂

A mass M is lowered with the help of a string by a distance x at a constant acceleration \(\frac { g }{ 2 } \). The magnitude of work done by the string will be 

(a)

Mgx

(b)

\(\frac { 1 }{ 2 } \) Mgx²

(c)

\(\frac { 1 }{ 2 } \)Mgx

(d)

Mgx²

A spring of force constant 800 Nm^-1 has an extension of 5 cm. The work done in extending it from 5 cm to 15 cm is

(a)

16 J

(b)

8 J

(c)

32 J

(d)

24 J

A running man has half the KE that a boy of half the mass of, the man. The man speeds up by 1 ms^-1  and then has the same KE as that of boy. The original speeds of man and boy in ms ^-1 are

(a)

\(\left( \sqrt { 2 } +1 \right) ,\left( \sqrt { 2 } -1 \right) \)

(b)

\(\left( \sqrt { 2 } +1 \right) ,\left( 2\sqrt { 2 } +1 \right)\)

(c)

\(\sqrt { 2 } ,\sqrt { 2 } \)

(d)

\(\left( \sqrt { 2 } +1 \right) ,\left( 2\sqrt { 2 } -1 \right)\)

A body of mass 10 kg moves with a constant speed v of 2 ms^-1 along a circular path of radius 8 m.~The power produced by the body will be 

(a)

10 Js^-1

(b)

98 Js^-1

(c)

49 Js^-1

(d)

zero

Given that the displacement of the body in metre is a function of time as follows x = 2t⁴ + 5.
The mass of the body is 2 kg. What is the increase in its kinetic energy one second after the start of motion?

(a)

8 J

(b)

16 J

(c)

32 J

(d)

64 J

Power applied to a particle varies with time as P = (3t - 2t + 1) W, where t is in second. Find the change in its kinetic energy between time t = 2 s and t = 4 s.

(a)

32 J

(b)

46 J

(c)

61 J

(d)

102 J

The potential energy of a particle of mass 1 kg is, U = 10 + (x - 2) ². Here U is in joule and x in Joule on the positive X-axis. Particle travels upto x = + 6 m. Choose the correct statement.

(a)

On negative X-axis particle travels upto x = - 2 m

(b)

The maximum kinetic energy of the particle is 16 J

(c)

Both (a} and (b) are correct

(d)

Both (a) and (b) are incorrect

If a body of mass M is moved from rest along a straight line by an engine which is delivering a constant power P, then the velocity of the body after time t will be

(a)

\(\frac { 2Pt }{ M } \)

(b)

\(\sqrt { \frac { 2\ Pt }{ M } } \)

(c)

\(\frac { Pt }{ 2M } \)

(d)

\( \sqrt { \frac { Pt }{ 2M } } \)

The energy possessed by a body by its state of strain is called as____________.

(a)

kinetic energy

(b)

mechanical energy

(c)

potential energy

(d)

none

On a frictionless surface, a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. After collision the first block moves at an angle θ to its initial direction and has a speed \(\frac{v}{3}\). The second block's speed after the collision  is _______________.

(a)

\(\frac{3}{\sqrt 2}v\)

(b)

\(\frac{\sqrt 3}{2}v\)

(c)

\(\frac{2\sqrt 2}{3}v\)

(d)

\(\frac{3}{4}v\)

A bullet of mass 10 g leaves a rifle at an initial velocity of 1000 m/s and strikes the earth at the same level with a velocity of 500 m/s, The work done in joule overcoming the resistance of air will be ___________.

(a)

375

(b)

3750

(c)

5000

(d)

500

Unit of work done _______________.

(a)

Nm

(b)

joule

(c)

either a or b

(d)

none

The amount of work done by a moving body depends on the ______________.

(a)

mass of the body

(b)

velocity

(c)

both (a) and (b)

(d)

time

The body must have a speed at highest point in vertical circular motion to stay in the circular path _____________.

(a)

\(\ge \sqrt { gr } \)

(b)

\(\ge \sqrt { 2gr } \)

(c)

\(\ge \sqrt { 5gr } \)

(d)

\(\ge\)5gr

kWh is the practical unit of _____________.

(a)

energy

(b)

power

(c)

electrical energy

(d)

none

If the two colliding bodies stick together after collision such collisions are ________________.

(a)

elastic collision

(b)

inelastic collision

(c)

perfectly inelastic collision

(d)

head on collision

If the velocity of separation is equal to the velocity of approach, then the collision is _______________.

(a)

conservative force

(b)

non conservative force

(c)

gravitational force

(d)

electrostatic force

A particle falls from a height h on a fixed horizontal plate and rebounds. If e is the coefficient of restitution, the total distance travelled by the particle on rebounding when it stops is _______________.

(a)

\(\frac { h{ \left( 1+e \right) }^{ 2 } }{ { \left( 1-e \right) }^{ 2 } } \)

(b)

\(\frac { h\left( 1+e \right) }{ \left( 1-e \right) } \)

(c)

\(\frac { h{ \left( 1+e \right) }^{ 2 } }{ 1-{ e }^{ 2 } } \)

(d)

\(\frac { h{ \left( 1-e \right) }^{ 2 } }{ { \left( 1+e \right) }^{ 2 } } \)

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same, which one of the following will not be affected?

(a)

M.I

(b)

 Angular momentum

(c)

 Angular velocity

(d)

Rotational K.E.

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity \(\omega \).The force exerted by the liquid at the other end is

(a)

M\(\omega \)²L/2

(b)

M\(\omega \)²L

(c)

M\(\omega \)²L/4

(d)

M\(\omega \)²L²/2

A thin circular ring of mass M and radius R is rotating about its axis with a constant angular velocity \(\omega \). Two objects each of mass m are attached gently to the ring. The wheel now rotates with an angular velocity

(a)

\(\frac { \omega M }{ (m+M) } \)

(b)

\(\frac { \omega (M-2m) }{ (M+2m) } \)

(c)

\(\frac { \omega M }{ (M+2m) } \)

(d)

\(\frac { \omega (M+2m) }{ M } \)

A particle of mass 5 g is moving with a uniform speed of 3\(\sqrt{2} cm/s\) in the x-y plane along the line y = 2\(\sqrt{5} cm\). The magnitude of its angular momentum about the origin in g-cm² /s is

(a)

zero

(b)

30

(c)

30 \(\sqrt{2}\)

(d)

30 \(\sqrt{10}\)

When a body is projected at an angle with the horizontal in the uniform gravitational field of the earth, the angular momentum of the body about the point of projection, as it proceeds along its path

(a)

remains constant

(b)

increases

(c)

decreases

(d)

initially decreases and after its highest point increases

A diver in a swimming pool bends his head before diving, because it

(a)

decreases his moment of inertia

(b)

decreases his angular velocity

(c)

increases his moment of inertia

(d)

decreases his linear velocity

A ring is kept on a rough inclined surface. But the coefficient of friction is less than the minimum value required for pure rolling. At any instant of time let K_T and K_R be the translational and rotational kinetic energies of the ring, then

(a)

K_R = K_T

(b)

K_R > K_T

(c)

K_T < K_R

(d)

K_R = 0

A particle performs uniform circular motion with an angular momentum L. If the frequency of the particle motion is doubled, the angular momentum becomes

(a)

2L

(b)

4L

(c)

\(\frac{L}{2}\)

(d)

\(\frac{L}{4}\)

If r denotes the distance between the sun and the earth, then the angular momentum of the earth around the sun is proportional to

(a)

r³/r

(b)

r

(c)

\(\sqrt{r}\)

(d)

r²

The figure shows a uniform rod lying along the x-axis. The locus of all the points lying on the x-y plane, about which the moment of inertia of the rod is same as that about O is

(a)

an ellipse

(b)

a circle

(c)

a parabola

(d)

a straight line

A particle of mass 1 kg is kept at (1m, 1m, 1m). The moment of inertia of this particle about Z-axis would be

(a)

1 kg- \(m^{ 2 }\)

(b)

2 kg-\(m^{ 2 }\)

(c)

3 kg- \(m^{ 2 }\)

(d)

None of these

Figure represents the moment of inertia of the solid sphere about an axis parallel to the diameter of the solid sphere and at a distance x from it. Which one of the following represents the variation of I with x ?

(a)

(b)

(c)

(d)

A cord is wound around the circumference of wheel of radius r The axis of the wheel is horizontal and MI is I. A weight mg is attached to the end of the cord and falls from rest. After falling through a distance h , the angular velocity of the wheel will be

(a)

\(\sqrt { \frac { 2gh }{ 1+mr^{ 2 } } } \)

(b)

\(\left( \frac { 2mgh }{ 1+mr^{ 2 } } \right) ^{ 1/2 }\)

(c)

\(\left( \frac { 2mgh }{ 1+2mr^{ 2 } } \right) ^{ 1/2 }\)

(d)

\(\sqrt { 2gh } \)

A mass m with velocity u strikes a wall normally and returns with the same speed. What is magnitude of the change in momentum of the body when it returns 

(a)

4 mu

(b)

mu

(c)

2 mu

(d)

zero

A undirectional force F varying with time t as shown in the figure acts on a body initially at rest for a short duration 2T.Then,the velocity acquired by the body is.

(a)

\(\frac { \pi { F }_{ 0 }T }{ 4m } \)

(b)

\(\frac { \pi { F }_{ 0 }T }{ 2m } \)

(c)

\(\frac { { F }_{ 0 }T }{ 4m } \)

(d)

zero

The dimension of torque is _____________.

(a)

ML²T²

(b)

M²L²T²

(c)

ML²T^-1

(d)

MLT^-2

A disc of radius R and mass M is rolling horizontally without slipping with a speed of 3 ms^-1 and moves up an inclined plane. The maximum height up to which the disc can reach is (g = 10 ms^-2) _____________.

(a)

0.675 m

(b)

0.325 m

(c)

0.275 m

(d)

0.825 m

A rod of length is 3m and its mass acting per unit length is directly proportional to distance x from one of its end then its centre of gravity from that end will be at _______________.

(a)

1.5 m

(b)

2 m

(c)

2.5 m

(d)

3.0 m

A point P consider at contact point of a wheel on ground which rolls on ground without slipping then value of displacement of point P when wheel completes half of rotation (If radius of wheel is 1 m) _____________.

(a)

2 m

(b)

\(\sqrt { { \pi }^{ 2 }+4 } \) m

(c)

\(\pi \)m

(d)

\(\sqrt { { \pi }^{ 2 }+2 } \) m.

A fly wheel rotating about fixed axis has a kinetic energy of 360 joule when its angular speed is 30 radian/sec, The moment of inertia of the wheel about the ax is of rotation is _____________.

(a)

0.6 kgm²

(b)

0.15 kgm²

(c)

0.8 kgm²

(d)

0.75 kgm²

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through ______________.

(a)

B

(b)

C

(c)

D

(d)

A

A wheel is rotating with angular velocity 2 rad/s. It is subjected to a uniform angular acceleration 2 rad/s² then the angular velocity after 10s is _____________.

(a)

12 rad/s

(b)

20 rad/s

(c)

22 rad/s

(d)

120 rad/s

The distance between the centres of carbon and oxygen atoms in the carbon monoxide gas molecule is 1.13 \(\overset{0}{A}\). The centre of mass of the molecule relative to oxygen atom is _______________.

(a)

0.602 \(\overset{0}{A}\)

(b)

0.527 \(\overset{0}{A}\)

(c)

1.13 \(\overset{0}{A}\)

(d)

0.565 \(\overset{0}{A}\)

Moment of inertia of a uniform solid cylinder about as axis passing perpendicular to the length and passing through the center is _______________.

(a)

MR²

(b)

M\(\left( \frac { { R }^{ 2 } }{ 2 } +\frac { { l }^{ 2 } }{ 12 } \right) \)

(c)

\(\frac { 1 }{ 2 } \)MR²

(d)

M\(\left( \frac { { R }^{ 2 } }{ 4 } +\frac { { l }^{ 2 } }{ 12 } \right) \)

If \(\overrightarrow {r}\) and \(\overrightarrow {F}\) are parallel or antiparallel, then the torque is _____________.

(a)

zero

(b)

minimum

(c)

maximum

(d)

infinity