A body starts moving from rest in straight line under a constant power source. Its displacement in time t is proportional to

(1) $t^{1/2}$

(2) t

(3) $t^{3/2}$

(4) $t^2$

A block of mass m = 25 kg on a smooth horizontal surface with a velocity $\overrightarrow{v}$ =3 $m{s}^{-1}$ meets the spring of spring constant k = 100 N/m fixed at one end as shown in the figure. The maximum compression of the spring and velocity of the block as it returns to the original position respectively are: 

1.  1.5 m, -3 $m{s}^{-1}$

2.  1.5 m, 0 $m{s}^{-1}$

3.  1.0 m, 3 $m{s}^{-1}$

4.  0.5 m, 2 $m{s}^{-1}$

The velocity, given to the block of mass (m), is $\sqrt{\frac{7}{2}gl}$to rotate it in a circle of radius l. Calculate the height (h) where the block leaves the circle.

1. $\frac{3l}{2}$

2. $\frac{4l}{3}$

3. $\frac{5l}{4}$

4. None of these

If length of string is $l\mathit{ }\mathit{=}\mathit{ }\frac{\mathit{10}}{\mathit{3}}m\mathit{,}\mathit{ }\frac{{\mathit{T}}_{\mathit{m}\mathit{a}\mathit{x}}}{{\mathit{T}}_{\mathit{m}\mathit{i}\mathit{n}}}\mathit{=}\mathit{4}$

$\mathrm{where}$
${\mathrm{T}}_{\max }= \mathrm{Maximum} \mathrm{tension} \mathrm{in} \mathrm{the} \mathrm{string}$
${\mathrm{T}}_{\min }=M\mathrm{inimum} \mathrm{tension} in \mathrm{the} \mathrm{string}.$
$\mathrm{Velocity} \mathrm{at} \mathrm{highest} \mathrm{point} \mathrm{is} -$

1.  10 m/s

2.  20 m/s

3.  $\frac{10}{\sqrt{2}}\mathrm{m}/\mathrm{s}$

4.  $10\sqrt{3} \mathrm{m}/\mathrm{s}$

The relation between velocity (v) and time (t) is $v\propto \sqrt{\mathrm{t}}$, then which one of the following quantity is constant?

1.  Force

2.  Power

3.  Momentum

4.  Kinetic Energy

A particle is moving on the circular path of the radius (R) with centripetal acceleration $a_c=k^{2}R{t}^2$. Then the correct relation showing power (P) delivered by net force versus time (t) is 

1. 1

2. 2

3. 3

4. 4

A projectile of mass 50 kg is shot vertically upwards with an initial velocity of 100ms^-1. After 5 seconds it explodes into two fragments, one of which having mass 20 kg, travels vertically up with a velocity of 150 ms^-1. The velocity of the other fragment at that instant is: [Take g= 9.8 m/$s^2$]

1.  100 ms^-1

2.  150 ms^-1

3.  -150 ms^-1

4.  -15 ms^-1

A steel wire can withstand a load up to 2940 N. A load of 150 kg is suspended from a rigid support. The maximum angle through which the wire can be displaced from the mean position, so that the wire does not break when the load passes through the position of equilibrium, is (2008 E)

1. 30$°$

2. 60$°$

3. 80$°$

4. 85$°$

A sphere of mass m moving with constant velocity hits another sphere of the same mass at rest. If e is the coefficient of restitution. The ratio of their velocities after the collision is

1.  1 + e

2.  $\frac{1 + \mathrm{e}}{2}$

3.  $\frac{1 + 2\mathrm{e}}{1 - 2\mathrm{e}}$

4.  $\frac{1 - \mathrm{e}}{1 + \mathrm{e}}$

A body is thrown vertically up with a certain initial velocity. The potential and the kinetic energy of the body are equal at a point P in its path. If the same body is thrown with double the velocity upwards, the ratio of the potential and the kinetic energies of the body when it crosses at the same point will be: 

1. 1:1

2. 1:4

3. 1:7

4. 1:8