A mass is performing a vertical circular motion (see figure.) If the average velocity of the particle is increased, then at which point the string will break?

     

1. A

2. B

3. C

4. D

The bob of a simple pendulum having length l, is displaced from the mean position to an angular position θ with respect to vertical. If it is released, then the velocity of the bob at the lowest position will be:

1. $\sqrt{2gl(1-\cos \theta )}$

2. $\sqrt{2gl(1+\cos }$ $\theta )$

3. $\sqrt{2gl}$ $\cos \theta$

4. $\sqrt{2gl}$

A ball is dropped from a height of \(5\) m. If it rebounds up to a height of \(1.8\) m, then the ratio of velocities of the ball after and before the rebound will be:
1. $\frac{3}{5}$

2. $\frac{2}{5}$

3. $\frac{1}{5}$

4. $\frac{4}{5}$ 

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 4 N force, its length is a metre and if 5 N is applied, its length is b metre. If 9 N 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%