A string is used to pull a block of mass m vertically up by a distance h at a constant acceleration $\frac{\mathrm{g}}{4}$. The work done by the tension in the string is

1. $+\frac{3\mathrm{mgh}}{4}$

2. $-\frac{\mathrm{mgh}}{4}$

3. $+\frac{5}{4}\mathrm{mgh}$

4. $+\mathrm{mgh}$

Work done by frictional force

1. is always negative

2. is always positive

3. is zero

4. May be positive, negative or zero

Two bodies of masses m₁ and m₂ have same kinetic energy. The ratio of their momentum is

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

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

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

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

Two bodies of masses m₁ and m₂ have same momentum. The ratio of their KE is

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

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

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

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

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