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%

If \(\pi=3.14,\) then the value of \({\pi}^{2}\) is

(a)

9.8596

(b)

9.860

(c)

9.86

(d)

9.9

A length-scale (I) depends on the permittivity (e) of a dielectric material,  Boltzmann constant (kB), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles. Which of the following expression for I is dimensionally correct?

(a)

\(l=\sqrt{{{nq^2}\over{\epsilon {k}_{B}T}}}\)

(b)

\(l=\sqrt{{{\epsilon {k}_{B}T}\over{nq^2}}}\)

(c)

\(l=\sqrt{{{q^2}\over{e{n}^{{{2}\over{3}}}{k}_{B}}T}}\)

(d)

\(l=\sqrt{{{q^2}\over{\epsilon n{k}_{B}T}}}\)

How many AU present in one light year?

(a)

6.30\(\times\)10⁴m

(b)

9.46\(\times\)10¹⁵m

(c)

6.2\(\times\)10²m

(d)

9.4\(\times\)10¹⁶m

The speed of an object v = 90km/h. The same quantity of speed in m/s is ______________.

(a)

90

(b)

25

(c)

45

(d)

180

3.5 kg mass of a metal plate has the volume of 1.5 m³. Find the density of metal plate ____________.

(a)

1.5 kg/m³

(b)

2.3 kg/m³

(c)

3.4 kg/m³

(d)

4.8 kg/m³

The value of 1^o is ______________.

(a)

1.745\(\times\)10^-2 rad

(b)

1.946\(\times\)10^-11 rad

(c)

3.6 rad

(d)

3600 rad

How many parsec are there in one kilometer?

(a)

3.084\(\times\)10^-16

(b)

3.084\(\times\)10⁸

(c)

3.24\(\times\)10^-14

(d)

None

What is the SI unit of Area?

(a)

m

(b)

m²

(c)

Nm^-1

(d)

cm^-1

Two resistors of resistances R₁ = 10 ± 0.3 ohm and R₂ = 20 ± 0.4 ohm are connected in parallel. The equivalent resistance of the parallel combination in ohm is ____________.

(a)

5.7 ± 0.1

(b)

15.2 ± 0.2

(c)

6.7 ± 0.2

(d)

9.5 ± 0.1

Identify the unit vector in the following?

(a)

\(\hat { i } +\hat { j } \)

(b)

\(\frac { \hat { i } }{ \sqrt { 2 } } \)

(c)

\(\hat { k } -\frac { \hat { j } }{ \sqrt { 2 } } \)

(d)

\(\frac { \hat { i } +\hat { j } }{ \sqrt { 2 } } \)

If the velocity is \(\overrightarrow { v } =2\hat { i } +{ t }^{ 2 }\hat { j } -9\overrightarrow { k } \), then the magnitude of acceleration at t = 0.5s is

(a)

1 ms^-2

(b)

2 ms^-2

(c)

zero

(d)

-1 ms^-2

If an object is dropped from the top of a building and it reaches the ground at t = 4 s, then the height of the building is (ignoring air resistance) (g = 9.8 ms^-2) 

(a)

77.3 m

(b)

78.4 m

(c)

80.5 m

(d)

79.2 m

A ball is dropped from some height towards the ground. Which one of the following represents the correct motion of the ball?

(a)

(b)

(c)

(d)

If a particle executes uniform circular motion, choose the correct statement

(a)

The velocity and speed are constant

(b)

The acceleration and speed are constant.

(c)

The velocity and acceleration are constant.

(d)

The speed and magnitude of acceleration are constant.

If an object is thrown vertically up with the initial speed u from the ground, then the time taken by the object  to return back to ground is

(a)

\(\frac{u^2}{2g}\)

(b)

\(\frac{u^2}{g}\)

(c)

\(\frac{u}{2g}\)

(d)

\(\frac{2u}{g}\)

An object is dropped in an unknown planet from height 50 m, it reaches the ground in 2 s. The acceleration due to gravity in this unknown planet is

(a)

g = 20 ms^-2

(b)

g = 25 ms^-2

(c)

g = 15 ms^-2

(d)

g = 30 ms^-2

Consider the quantities pressure, power, energy, impulse, charge. Out of these, the only vector quantity is _______________.

(a)

pressure

(b)

power

(c)

impulse

(d)

charge

The length of a vector is _______________

(a)

always a negative quantity

(b)

always a positive quantity

(c)

either positive or negative

(d)

denoted by '\(\lambda \)' 

Distance is a scalar quantity and ______________ is a vector.

(a)

Speed

(b)

Length

(c)

Time

(d)

Displacement

Two masses m₁ and m₂ are experiencing the same force where m₁ < m₂.The ration of their acceleration \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } \) is _____________.

(a)

1

(b)

less than 1

(c)

greater than 1

(d)

all the three cases

Choose appropriate free body diagram for the particle experiencing net acceleration along negative y direction. (Each arrow mark represents the force acting on the system).

(a)

(b)

(c)

(d)

Choose the correct statement from the following

(a)

Centrifugal and centripetal forces are action reaction pairs

(b)

Centripetal forces is a natural force

(c)

Centrifugal force arises from gravitational force

(d)

Centripetal force acts towards the center and centrifugal force appears to act away from the center in a circular motion.

In a rocket, the fuel burns at the rate of 1 kg s^-1. This fuel burnt eject gases at a speed of 90 km s^-1. The force exerted on the rocket is, ________________.

(a)

45000 N

(b)

90000 N

(c)

60000 N

(d)

10000 N

A ball of 300 g mass moving with a speed of 20 m/s rebounds after striking normally a perfectly elastic wall. The change in momentum of a ball is ______________.

(a)

12 kg ms^-1

(b)

-12 kg ms^-1

(c)

6 kg ms^-1

(d)

-6 kg ms^-1

A constant retarding force of 60 N is applied to a body of mass 25 kg moving with a speed of 20 ms^-1 How long does the body take to stop?

(a)

8.33 seconds

(b)

7.58 seconds

(c)

4 seconds

(d)

5.8 seconds

How many degrees make a one newton?

(a)

10² dyne

(b)

20² dyne

(c)

10⁵ dyne

(d)

20⁵ dyne

A force of 2.5 N acts on a body of mass 10 g. What is the acceleration of the body?

(a)

1.5\(\times\)10² ms^-2

(b)

2.0\(\times\)10³ ms^-2

(c)

2.5\(\times\)10³ ms^-2

(d)

3.0\(\times\)10² ms^-2

A block B is pushed momentarily along a horizontal surface with initial velocity v- μ coefficient of friction between B and surface, block B will come to rest after a time ___________.

(a)

v/gμ

(b)

gμ/v

(c)

g/v

(d)

v/g

If the amount of work done by a force depends only on the initial and final positions of the object which has been moved, then such a force is called ______________.

(a)

gravitation

(b)

conservative

(c)

Retarding

(d)

Non conservative

A uniform force of (2\(\hat { i }\)+\(\hat { j }\)) N acts on a particle of mass 1 kg. The particle displaces from position (3\(\hat { j }\)+\(\hat { k }\)) m to (5\(\hat { i }\)+3\(\hat { j }\)) m. The work done by the force on the particle is

(a)

9 J

(b)

6 J

(c)

10 J

(d)

12 J

A body of mass 4 m is lying in xy-plane at rest. It suddenly explodes into three pieces. Two pieces each of mass m move perpendicular to each other with equal speed v. The total kinetic energy generated due to explosion is

(a)

mv²

(b)

\(\frac{3}{2}\)mv²

(c)

2mv²

(d)

4mv²

The potential energy of a system increases, if work is done

(a)

by the system against a conservative force

(b)

by the system against a non-conservative force

(c)

upon the system by a conservative force

(d)

upon the system by a non- conservative force

The work done by the conservative force for a closed path is

(a)

always negative

(b)

zero

(c)

always positive

(d)

not defined

If the linear momentum of the object is increased by 0.1% then the kinetic energy is Increased by

(a)

0.1 %

(b)

0.2 %

(c)

0.4 %

(d)

0.01 %

If the potential energy of the particle is \(\alpha -\frac { \beta }{ 2 } { x }^{ 2 }\), then force experienced by the particle is

(a)

F = \(\frac { \beta }{ 2 } { x }^{ 2 }\)

(b)

F = βx

(c)

F = -βx

(d)

F = -\(\frac { \beta }{ 2 } { x }^{ 2 }\)

Two equal masses m₁ and m₂ are moving along the same straight line with velocities 5ms^-1 and -9 ms^-1 respectively. If the collision is elastic, then calculate the velocities after the collision of m₁ and m₂ respectively

(a)

-4 ms^-1 and 10 ms^-1

(b)

10 ms^-1 and 0 ms^-1

(c)

-9 ms^-1 and 5 ms^-1

(d)

5 ms^-1 and 1 ms^-1

A particle is placed at the origin and a force F = kx is acting on it (where k is a positive constant). If U (0) = 0, the graph of U(x) versus x will be (where U, is the potential , energy function)

(a)

(b)

(c)

(d)

A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then, the long piece will have a force constant of

(a)

\(\frac{2}{3}\)k

(b)

\(\frac{3}{2}\)k

(c)

3k

(d)

6k

An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit length of the water of the jet. What is the rate at which kinetic energy is imparted to water?

(a)

\({{1}\over{2}}{m}{v}^{2}\)

(b)

mv³

(c)

\({{1}\over{2}}{m}{v}^{3}\)

(d)

\({{1}\over{2}}{m}{v}^{2}\)

The center of mass of a system of particles does not depend upon,

(a)

position of particles

(b)

relative distance between particles

(c)

masses of particles

(d)

force acting on particle

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force 30 N?

(a)

0.25 rad s^-2

(b)

25 rad s^-2

(c)

5 ms^-2 

(d)

25 ms^-2

A closed cylindrical container is partially filled with water. As the container rotates in a horizontal plane about a perpendicular bisector, its moment of inertia

(a)

increases

(b)

decreases

(c)

remains constant

(d)

depends on direction of rotation

A rigid body rotates with an angular momentum L. If its kinetic energy is halved, the angular momentum becomes,

(a)

L

(b)

L/2

(c)

2L

(d)

L/\(\sqrt{2}\)

A particle undergoes uniform circular motion. The angular momentum of the particle remain conserved about,

(a)

the center point of the circle

(b)

the point on the circumference of the circle

(c)

any point inside the circle

(d)

any point outside the circle

A disc of the moment of inertia I_a is rotating in a horizontal plane about its symmetry axis with a constant angular speed \(\omega\). Another disc initially at rest of moment of inertia I_b is dropped coaxially on to the rotating disc. Then, both the discs rotate with the same constant angular speed. The loss of kinetic energy due to friction in this process is,

(a)

\(\frac { 1 }{ 2 } \frac { { I }_{ b }^{ 2 } }{ 2({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

(b)

\(\frac { { I }_{ b }^{ 2 } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

(c)

\(\frac { { ({ I }_{ b }-{ I }_{ a }) }^{ 2 } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

(d)

\(\frac { 1 }{ 2 } \frac { { { I }_{ b }{ I }_{ b } } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

The ratio of the acceleration for a solid sphere (mass m and radius R) rolling down an incline of angle \(\theta\) without slipping and slipping down the incline without rolling is,

(a)

5: 7

(b)

2: 3

(c)

2: 5

(d)

7: 5

The speed of a solid sphere after rolling down from rest without sliding on an inclined plane of vertical height h is,

(a)

\( \sqrt \frac{4}{3}gh\)

(b)

\( \sqrt \frac{10}{7}gh\)

(c)

\(\sqrt{2gh}\)

(d)

\( \sqrt \frac{1}{2}gh\)

The speed of the center of a wheel rolling on a horizontal surface is v_o.  A point on the rim in level with the center will be moving at a speed of,

(a)

zero

(b)

v_o

(c)

\(\sqrt{2}\)v_o

(d)

2v_o

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along

(a)

a line perpendicular to the plane of rotation

(b)

the line making an angle of 45^o to the plane of rotation

(c)

the radius

(d)

tangent to the path

If the masses of the Earth and Sun suddenly double, the gravitational force between them will

(a)

remain the same

(b)

increase 2 times

(c)

increase 4 times

(d)

decrease 2 times

A planet moving along an elliptical orbit is closest to the Sun at distance r₁ and farthest away at a distance of r₂. If v₁ and v₂ are linear speeds at these points respectively. Then the ratio \({v_1\over v_2}\) is

(a)

\({r_2\over r_1}\)

(b)

\(({r_2\over r_1})^2\)

(c)

\({r_1\over r_2}\)

(d)

\(({r_1\over r_2})^2\)

If the distance between the Earth and Sun were to be doubled from its present value, the number of days in a year would be

(a)

64.5

(b)

1032

(c)

182.5

(d)

730

According to Kepler’s second law, the radial vector to a planet from the Sun sweeps out equal areas in equal intervals of time. This law is a consequence of

(a)

conservation of linear momentum

(b)

conservation of angular momentum

(c)

conservation of energy

(d)

conservation of kinetic energy

The gravitational potential energy of the Moon with respect to Earth is

(a)

always positive

(b)

always negative

(c)

can be positive or negative

(d)

always zero

The work done by the Sun’s gravitational force on the Earth is

(a)

always zero

(b)

always positive

(c)

can be positive or negative

(d)

always negative

If the mass and radius of the Earth are both doubled, then the acceleration due to gravity g'

(a)

remains same

(b)

\({g\over 2}\)

(c)

2g

(d)

4g

If a person moves from Chennai to Trichy, his weight

(a)

increases

(b)

decreases

(c)

remains same

(d)

increases and then decreases

If the acceleration due to gravity becomes 4 times its original value, then escape speed

(a)

remains same

(b)

2 times of original value

(c)

becomes halved

(d)

4 times of original value

The kinetic energy of the satellite orbiting around the Earth is

(a)

equal to potential energy

(b)

less than potential energy

(c)

greater than kinetic energy

(d)

zero