A particle is moving under the influence of a force given by F = kx, where k is a constant and x is the distance moved. The energy (in joules) gained by the particle in moving from x = 0 to x = 3 is

• 2 k

• 3.5 k

• 4.5 k

• 9 k

The work done in moving an alpha particle between two points having potential difference 25 V is

• 8 × 10^-18 J

• 8 × 10^-19 J

• 8 × 10^-20 J

• 8 × 10^-16 J

A rod AB of mass 10 kg and length 4 m rests on a horizontal floor with end A fixed so as to rotate it in vertical plane about perpendicular axis passing through A. If the work done on the rod is 100 J, the height to which the end B be raised vertically above the floor is

• 1.5 m

• 2.0 m

• 1.0 m

• 2.5 m

A particle is released from a height S. At certain height its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively

• $\frac{\mathrm{S}}{4}, \frac{3\mathrm{gS}}{2}$

• $\frac{\mathrm{S}}{4}, \frac{\sqrt{3\mathrm{gS}}}{2}$

• $\frac{\mathrm{S}}{2}, \frac{3\mathrm{gS}}{2}$

• $\frac{\mathrm{S}}{4}, \sqrt{\frac{3\mathrm{gS}}{2}}$

An electric pump is used to fill an overhead tank of capacity 9 m³ kept at a height of 10 m above the ground. If the pump takes 5 min to fill the tank by consuming 10 kW power, the efficiency of the pump should be (Take g = 10 ms^-2)

• 60 %

• 40 %

• 20 %

• 30 %

Potential energy in a spring when stretched by 2 cm is U. Its potential energy, when stretched by 10 cm is

• $\frac{\mathrm{U}}{25}$

• $\frac{\mathrm{U}}{5}$

• 25 U

• 5 U

47.

A running man has the same kinetic energy as that of a boy of half his mass. The man speeds up by 2 ms^-1 and the boy changes his speed by x ms^-1, so that the kinetic energies of the boy and the man are again equal. Then x in ms^-1 is

• $- 2\sqrt{2}$

• $+ 2\sqrt{2}$

• $\sqrt{2}$

• 2

Two cars A and B are travelling in the same direction with velocities v₁ and v₂ (v₁ > v₂). When the car A is at a distance d behind the car B, the driver of the car A applies the brake producing uniform retardation, a. There will be no collision when

• $\mathrm{d} < \left(\frac{{\mathrm{v}}_1 - {\mathrm{v}}_2}{2\mathrm{a}}\right)$

• $\mathrm{d} > \frac{{{\mathrm{v}}_1}^2 - {{\mathrm{v}}_2}^2}{2\mathrm{a}}$

• $\mathrm{d} > \frac{{\left({\mathrm{v}}_1 - {\mathrm{v}}_2\right)}^2}{2\mathrm{a}}$

• $\mathrm{d} < \frac{{{\mathrm{v}}_1}^2 - {{\mathrm{v}}_2}^2}{2\mathrm{a}}$

The momentum of a body is increased by 25%. The kinetic energy is increased by about 

• 25 %

• 5 %

• 56 %

• 38 %

A particle is displaced from a position $\left(2\hat{\mathrm{i}} - \hat{\mathrm{j}} + \hat{\mathrm{k}}\right)$ to another position $\left(3\hat{\mathrm{i}} + 2\hat{\mathrm{j}} - 2\hat{\mathrm{k}}\right)$ under the action of the force of $\left(2\hat{\mathrm{i}} + \hat{\mathrm{j}} - \hat{\mathrm{k}}\right)$. The work done by the force in an arbitrary unit is

• 8

• 10

• 12

• 16