Work Done When Force Is Varying

Q. A locomotive of mass m starts moving so that its velocity varies according to the law v = a$\sqrt{s}$, where a is a constant, and s is the distance covered. Find the total work performed by all the forces which are acting on the locomotive during the first t seconds after the beginning of motion.

1. ma⁴t²/8
2. ma³t²/4
3. ma⁴t²/4
4. ma³t²/8

Q. A body of mass 6kg is under a force which causes displacement in it given by $S=\frac{t^2}{4}$ metres where t is time. The work done by the force in 2 seconds is

1. 6 J
2. 12 J
3. 3 J
4. 9 J

Q.

The displacement x of a particle moving in one dimension under the action of a constant force is related to the time t by the equation, t = $\sqrt{x}$ + 3 where x is in meters and t is in seconds. The work done by the force in the first 6 seconds is

1. 9 J

2. 6 J

3. 0 J

4. 3 J

Q.

A body of mass 3 kg is under a force, which causes a displacement in it is given by $S=\frac{t^3}{3}$ (in m). Find the work done by the force in first 2 seconds

1. 3.8 J

2. 5.2 J

3. 24 J

4. 2 J

Q.

A particle moves under the effect of a force F = Cx from x = 0 to $x=x_1$ . The work done in the process is

1. 

2. 

3. 

4. Zero

Q.

A metallic wire of length L metres extends by l metres when stretched by suspending a weight Mg to it. The mechanical energy stored in the wire is

1. 

2. 

3. 

4. 

Q.

The relationship between force and position is shown in the figure given (in one dimensional case). The work done by the force in displacing a body from x = 1 cm to x = 5 cm is

1. 60 ergs

2. 70 ergs

3. 20 ergs

4. 700 ergs

Q.

A position dependent force $F=7-2x+3x^2$ acts on a small body of mass 2 kg and displaces it from x = 0 to x = 5m. The work done in joules is

1. 70

2. 35

3. 270

4. 135

Q.

Given $\overrightarrow{F}=\left(x{y}^2\right)\hat{i}+\left(x^{2}y\right)\hat{j}N$. The work done by $\overrightarrow{F}$ when a particle is taken along the semicircular path OAB where the coordinates of B are (4, 0) is

1. 

2. 

3. 

4. 

Q.

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

1. $a{L}^2+b{L}^3$

2. $\frac{1}{2}(a{L}^2+b{L}^3)$

3. $\frac{a{L}^2}{2}+\frac{b{L}^3}{3}$

4. $\frac{1}{2}(\frac{a{L}^2}{2}+\frac{b{L}^3}{3})$