A block of mass m is pulled along a circular arc by means of a constant horizontal force F as shown. Work done by this force in pulling the block from A to B is

1. $\frac{\mathrm{FR}}{2}$

2. FR

3. $\frac{\sqrt{3}}{2}$FR

4. mgR

A particle is displaced from a position $(2\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})$ metre to another position $(3\hat{\mathrm{i}}+2\hat{\mathrm{j}}-2\hat{\mathrm{k}})$ metre under the action of force $(2\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}})$N. Work done by the force is

1. 8 J

2. 10 J

3. 12 J

4. 36 J

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