Which one of the following Cartesian coordinate systems is not followed in physics?

(a)

(b)

(c)

(d)

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)

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

Which one of the following physical quantities cannot be represented by a scalar?

(a)

Mass

(b)

length

(c)

momentum

(d)

magnitude of acceleration

If a particle has negative velocity and negative acceleration, its speed

(a)

increases

(b)

decreases

(c)

remains same

(d)

zero

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

If a particle executes uniform circular motion in the xy plane in clock wise direction, then the angular velocity is in

(a)

+y direction

(b)

+z direction

(c)

-z direction

(d)

-x direction

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)

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

Two objects are projected at angles 30° and 60° respectively with respect to the horizontal direction. The range of two objects are denoted as R_30° and R_30°. Choose the correct relation from the following

(a)

R_30° = R_60°

(b)

R_30° = 4R_60°

(c)

R_30° =\(\frac{R_{60°}}{2}\)

(d)

R_30° = 2R_60°

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

Which one of the following satatement is true?

(a)

A scalar quantity is conserved in a process

(b)

A scalar quantity does not vary from one point to another in apace

(c)

A scalar quantity can never take -ve values

(d)

A scalar quantity has only magnitude and no direction.

The angle between A i +j and B = i - j is ______________.

(a)

45°

(b)

90°

(c)

-45°

(d)

180°

The component of position vector \(\overrightarrow { r } \) along x-axis will maximum value if ____________

(a)

\(\overrightarrow { r } \) is along the x - axis

(b)

\(\overrightarrow { r } \) makes an angle of 45° with x - axis

(c)

\(\overrightarrow { r } \)  is along the y - axis

(d)

\(\overrightarrow { r } \)  is along - ve y - axis 

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

The horizontal range of a projectile fired at an angle of 15° is 50 m. If it is fired with the same speed at angle of 45°, its range will be

(a)

125 m

(b)

75 m

(c)

100 m

(d)

150 m

Choose the motion in two dimension from the following.

(a)

Motion of a train along a straight railway track

(b)

An object falling freely under gravity close to the Earth.

(c)

A particle moving along a curved path in a plane.

(d)

Flying of a kite on a windy day.

A particle moves with uniform velocity. Which of the following statements about the motion of the particle is true?

(a)

Its speed is zero

(b)

Its acceleration is zero

(c)

Its acceleration is opposite to the velocity

(d)

Its speed may be variable

A body is allowed to fall from a height of 100 m. If the time taken for the first 50m is t₁, and for the remaining 50m is t₂, then ________________

(a)

t₁ = t₂

(b)

t₁ > t₂

(c)

t₁ < t₂

(d)

depends upon the mass

Two cars P and Q start fun a point at the same time in a straight line and their positions are represented by X p(t) = (at + bt²) and x_Q(t) = (ft - ft²). At what time do the cars have the same velocity?

(a)

\({a-f\over l+b}\)

(b)

\({a+f\over2(b-1)}\)

(c)

\({a+f\over2(l+b)}\)

(d)

\({f-a\over2(b-1)}\)

If the velocity of a particle is v= At + Bt², where A and B are constants, then the distance travelled by it between 1 s and 2 s is _______________.

(a)

\({3\over2}A+{7\over3}B\)

(b)

\({A\over2}+{B\over3}\)

(c)

\({3\over2}A+4B\)

(d)

\(3A+7B\)

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v(x) = \(\beta\) x^-2n , where \(\beta\) and n are constants and x is the position of the particle. The acceleration of the particle as a function of x, is given by

(a)

-2\(\beta\)² x^-2n+1

(b)

\(-2n\beta ^2e^{-4n+1}\)

(c)

\(-2n\beta ^2x^{-2n-1}\)

(d)

\(-2n\beta ^2e^{-4n-1}\)

A stone falls freely under gravity. It covers distances h₁, h₂ and h₃ in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h₁, h₂ and h₃is ____________.

(a)

h₂ = 3h₁ and h₃ = 3h₂

(b)

h₁ = h₂ = h₃

(c)

h₁ = 2h₂ = h₃

(d)

\(h_1={h_2\over 3}={h_3\over 5}\)

The displacement 'x' (in meter) of a particle of mass 'm' (in kg) moving in one dimension under the action of a force, is related to time 't' (in sec) by t = \(\sqrt{x}\) + 3 . The displacement of the particle when its velocity is zero, will be ____________.

(a)

4m

(b)

0m(zero)

(c)

6m

(d)

2m