Post Video Test - Work Power and EnergyContact Number: 9667591930 / 8527521718

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1.

When a rubber band is stretched by a distance x, it exerts a restoring force of magnitude $\mathrm{F}=\mathrm{ax}+{\mathrm{bx}}^{2}$, where a and b are constants. The work done in stretching the unstretched rubber band by L is

1. ${\mathrm{aL}}^{2}+{\mathrm{bL}}^{3}$

2. $\frac{1}{2}\left({\mathrm{aL}}^{2}+{\mathrm{bL}}^{3}\right)$

3. $\frac{{\mathrm{aL}}^{2}}{2}+\frac{{\mathrm{bL}}^{3}}{3}$

4. $\frac{1}{2}\left(\frac{{\mathrm{aL}}^{2}}{2}+\frac{{\mathrm{bL}}^{3}}{3}\right)$

2.

A force $\mathrm{F}=-\mathrm{k}\left(\mathrm{y}\hat{\mathrm{i}}+\mathrm{x}\hat{\mathrm{j}}\right)$(where k is a positive constant) acts on a particle is moving in the x-y plane. Starting from the origin, the particle is taken along the positive X-axis to the point (a,0) and then parallel to the Y-axis to the point (a,a). The total work done by the force F on the particle is

1. $-2{\mathrm{ka}}^{2}$

2. $2{\mathrm{ka}}^{2}$

3. $2{\mathrm{ka}}^{2}$

4. ${\mathrm{ka}}^{2}$

3.

A uniform chain of length L and mass M is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity , the work required to pull the hanging part on to the table is

1. MgL

2. MgL/3

3. MgL/9

4. MgL/18

4.

A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to

1. ${\mathrm{t}}^{1/2}$

2. ${\mathrm{t}}^{3/4}$

3. ${\mathrm{t}}^{3/2}$

4. ${\mathrm{t}}^{2}$

5.

An ideal spring with spring constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum exention in the spring is

1. $\frac{4\mathrm{Mg}}{\mathrm{k}}$

2. $\frac{2\mathrm{Mg}}{\mathrm{k}}$

3. $\frac{\mathrm{Mg}}{\mathrm{k}}$

4. $\frac{\mathrm{Mg}}{2\mathrm{k}}$

6.

A particle, which is constrained to move along x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F (x) = $-\mathrm{kx}+{\mathrm{ax}}^{3}$. Here, k and a are positive constants. For x$\ge $0, the functional form of the potential energy U (x) of the particle is

1.

2.

3.

4.

7.

A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to

1. $\mathrm{v}$

2. ${\mathrm{v}}^{2}$

3. ${\mathrm{v}}^{3}$

4. ${\mathrm{v}}^{4}$

8.

A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then, the long piece will have a force constant of

1. (2/3) k

2. (3/2) k

3. 3 k

4. 6 k

9.

A particle moves in a straight line with retardation proportional to its displacement. The loss of kinetic energy during a displacement x is proportional to

1. ${\mathrm{x}}^{2}$

2. ${\mathrm{e}}^{\mathrm{x}}$

3. $\mathrm{x}$

4. ${\mathrm{log}}_{e}x$

10.

The potential energy of a 1 kg particle free to move along the x-axis is given by U(x) = $\left(\frac{{\mathrm{x}}^{4}}{4}-\frac{{\mathrm{x}}^{2}}{2}\right)J$

The total mechanical energy of the particle is 2 J. Then, the maximum speed in (m/s) is

1. $1/\sqrt{2}$

2. $2$

3. $3/\sqrt{2}$

4. $\sqrt{2}$

11.

A uniform chain has a mass M and length L. It is placed on a frictionless table with length ${\mathrm{l}}_{0}$ hanging over the edge. The chain begins to slide down. Then the speed v with which the end slides away from the edge is given by

1. $\mathrm{v}=\sqrt{\frac{\mathrm{g}}{\mathrm{L}}(\mathrm{L}+{\mathrm{l}}_{0})}$

2. $\mathrm{v}=\sqrt{\frac{\mathrm{g}}{\mathrm{L}}(\mathrm{L}-{\mathrm{l}}_{0})}$

3. $\mathrm{v}=\sqrt{\frac{\mathrm{g}}{\mathrm{L}}({\mathrm{L}}^{2}-{\mathrm{L}}_{0}^{2})}$

4. $\mathrm{v}=\sqrt{2\mathrm{g}\left(\mathrm{L}-{\mathrm{l}}_{0}\right)}$

12.

$\overrightarrow{\mathrm{F}}={x}^{3}{y}^{2}\hat{i}+{x}^{2}{y}^{3}\hat{j}$. The work done by the variable force along OA

1. $\frac{{\mathrm{a}}^{2}}{4}$

2. zero

3. $\frac{{\mathrm{a}}^{6}}{6}$

4. $\frac{{\mathrm{a}}^{6}}{8}$

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