A particle of mass m₁ is moving with a velocity v₁ and another particle of mass m₂ is moving with a velocity v₂. Both of them have the same momentum, but their kinetic energies are E₁ and E₂ respectively. If m₁ > m₂ then: 

1. $\frac{{\mathrm{E}}_1}{{\mathrm{E}}_2}=\frac{{\mathrm{m}}_1}{{\mathrm{m}}_2}$

2. ${\mathrm{E}}_1>{\mathrm{E}}_2$

3. ${\mathrm{E}}_1={\mathrm{E}}_2$

4. ${\mathrm{E}}_1<{\mathrm{E}}_2$

A mass of 0.5 kg moving with a speed of 1.5 m/s on a horizontal smooth surface, collides with a nearly weightless spring with force constant k = 50 N/m. The maximum compression of the spring would be :-
           
1. 0.12 m

2. 1.5 m

3. 0.5 m

4. 0.15 m 

If two springs, A and B $(K_A = 2 K_B),$ are stretched by the same suspended weights, then the ratio of work done in stretching is equal to:
1.  1 : 2
2.  2 : 1
3.  1 : 1
4.  1 : 4

When a spring is subjected to 4N force, its length is a metre and if 5N is applied, its length is b metre. If 9N is applied, its length will be:

1.  4b – 3a

2.  5b – a

3.  5b – 4a

4.  5b – 2a

A body initially at rest and sliding along a frictionless track from a height h (as shown in the figure) just completes a vertical circle of diameter AB = D. The height h is equal to: 
            

1. $\frac{3}{2}D$

2. D

3. $\frac{7}{4}D$

4. $\frac{5}{4}D$

If a stone is projected vertically upward from the ground at a speed of 10 m/s, then it's: (g = 10 $\mathrm{m}/{\mathrm{s}}^2$)

1.  Potential energy will be maximum after 0.5 s

2.  Kinetic energy will be maximum again after 1 s

3.  Kinetic energy = potential energy at a height of 2.5 m from the ground

4.  Potential energy will be minimum after 1 s

The kinetic energy of a body is increased by 21%. The percentage increase in the magnitude of linear momentum of the body will be:

1.  10%

2.  20%

3.  Zero

4.  11.5%

A rigid body of mass 'm' is moving in a circle of radius 'r' with constant speed 'v'. The force on the body is $\frac{{\mathrm{mv}}^2}{\mathrm{r}}$ and is always directed towards the center. The work done by this force in moving the body over half the circumference of the circle will be:

1.  $\frac{{\mathrm{mv}}^2}{\mathrm{r\pi }}$

2.  ${\mathrm{mr}}^2\mathrm{\pi }$

3.  Zero

4.  $2{\mathrm{mv}}^2\mathrm{\pi }$

A particle of mass 10 kg moves with a velocity of $10\sqrt{x}$ SI units, where x is displacement. The work done by the net force during the displacement of the particle from x = 4 m to x = 9 m is:

1.  1250 J

2.  1000

3.  3500 J

4.  2500 J

The potential energy of a particle of mass m varies as the magnitude of the $U=a{x}^2+by.$ The magnitude of the acceleration of the particle at (0, 3) is: (symbols have their usual meaning)

1.  $\sqrt{\frac{\mathrm{b}}{\mathrm{m}}}$

2.  $\sqrt{\frac{3\mathrm{b}}{\mathrm{m}}}$

3.  $\frac{\mathrm{b}}{\mathrm{m}}$

4.  Zero