Work Done When Path Is Not Straight

Q.

A body of mass m is moving in a circle of radius r with a constant speed v. The force on the body is $\frac{m{v}^2}{r}$and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle

1. Zero

2. 

3. 

4. 

Q.

A force $F=-K(yi+aj)$ (where K is a positive constant) acts on a particle moving in the xy-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 particles is

1. 

2. 

3. 

4. 

Q.

A body of mass m is moving in a circle of radius r with a constant speed v. The force on the body is $\frac{m{v}^2}{r}$ and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle

1. $\frac{m{v}^2}{\pi r^2}$

2. Zero

3. $\frac{m{v}^2}{r^2}$

4. $\frac{\pi r^2}{m{v}^2}$

Q.

A particle of mass 0.1 kg is subjected to a force which varies with distance as shown in the figure. If it starts its journey from rest at x = 0, its velocity at x = 12 m is

1. Zero

2. $20\sqrt{2}m/s$

3. $20\sqrt{3}m/s$

4. $40m/s$

Q. A particle is moved from $(0,0)$ to $(a,a)$ under a force $\overrightarrow{F}=(3\hat{i}+4\hat{j})$ from two paths. Path $1$ is $OP$ and path $2$ is $OQP$. Let $W_1$ and $W_2$ be the work done by this force along respective paths. Then

1. $W_1=W_2$
2. $W_1=2W_2$
3. $W_2=2W_1$
4. $W_2=4W_1$

Q. A small body of mass $m=0.10kg$ moves in the reference frame rotating about a stationary axis with constant angular velocity $\omega =5.0rad/s$. What work does the centrifugal force of inertia perform during the transfer of this body along an arbitrary path from point $1$ to point $2$ which are located at the distance $r_1=30cm$ and $r_2=50cm$ from the axis of rotation?

1. $0.15J$
2. $0.4J$
3. $0.2J$
4. $0.35J$

Q. A force $F=-K(y\hat{i}+x\hat{j})$ (where $K$ is a positive constant) acts on a particle moving in the xy-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 particles is

1. $-2K{a}^2$
2. $2K{a}^2$
3. $-K{a}^2$
4. $K{a}^2$