Two bodies of masses m₁ and m₂ are moving with same kinetic energy. If P₁ and P₂ are their respective momentum, the ratio $\frac{{\mathrm{P}}_1}{{\mathrm{P}}_2}$ is equal to

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

2. $\sqrt{\frac{{\mathrm{m}}_2}{{\mathrm{m}}_1}}$

3. $\sqrt{\frac{{\mathrm{m}}_1}{{\mathrm{m}}_2}}$

4. $\frac{{{\mathrm{m}}_1}^2}{{{\mathrm{m}}_2}^2}$

A particle moves along X-axis from x=0 to x=1 m under the influence of a force given by $\mathrm{F}=3{\mathrm{x}}^2+2\mathrm{x}-10$. Work done in the process is

1. +4 J

2. -4 J

3. +8 J

4. -8 J

Under the action of a force, a 2 kg body moves such that its position x as a function of time t is given by $\mathrm{x}=\frac{{\mathrm{t}}^2}{3}$, where x is in metre and t in second. The work done by the force in first two seconds is

1. 1600 J

2. 160 J

3. 16 J

4. $\frac{16}{9}$J

KE acquired by a mass m intravelling a certain distance d, starting from rest, under the action of a constant force F is

1. Directly proportional to $\sqrt{\mathrm{m}}$

2. Directly proportional to m

3. Directly proportional to $\frac{1}{\mathrm{m}}$

4. None of these

The total work done on a particle is equal to the change in its kinetic energy. This is applicable 

1. Always

2. Only if the conservative forces are acting on it

3. Only in inertial frames

4. Only when pseudo forces are absent

A particle of mass 0.1 kg is subjected to a force which varies with distance as shown. If it starts its journey from rest at x=0, then its velocity at x=12 m is

1. 0 m/s

2. $20\sqrt{2}$m/s

3. $20\sqrt{3}$m/s

4. 40 m/s

Potential energy is defined:

A stick of mass m and length l is pivoted at one end and is displaced through an angle $\mathrm{\theta }$. The increase in potential energy is 

1. $\mathrm{mg}\frac{\mathrm{l}}{2}(1-\mathrm{cos\theta })$

2. $\mathrm{mg}\frac{\mathrm{l}}{2}(1+\mathrm{cos\theta })$

3. $\mathrm{mg}\frac{\mathrm{l}}{2}(1-\mathrm{sin\theta })$

4. $\mathrm{mg}\frac{\mathrm{l}}{2}(1+\mathrm{sin\theta })$

A spring with spring constants k when compressed by 1 cm, the potential energy stored is U. If it is further compressed by 3 cm, then change in its potential energy is

1. 3U

2. 9U

3. 8U

4. 15U

Two springs have force constant K₁ and K₂ (K₁>K₂). Each spring is extended by same force F. If their elastic potential energy are E₁ and E₂ then $\frac{{\mathrm{E}}_1}{{\mathrm{E}}_2}$ is

1. $\frac{{\mathrm{K}}_1}{{\mathrm{K}}_2}$

2. $\frac{{\mathrm{K}}_2}{{\mathrm{K}}_1}$

3. $\sqrt{\frac{{\mathrm{K}}_1}{{\mathrm{K}}_2}}$

4. $\sqrt{\frac{{\mathrm{K}}_2}{{\mathrm{K}}_1}}$