Work Done When Path Is Not Straight

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 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 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. $-2K{a}^2$

2. $2K{a}^2$

3. $-K{a}^2$

4. $K{a}^2$

Q.

A block of mass 2kg is released from A on the track that is one quadrant of a circle of radius 1m. It slides down the track and reaches B with a speed of and finally stops at C at a distance of 3m from . The work done against the force of friction is

1. 10 J

2. 20 J

3. 2 J

4. 6 J

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. $0.35J$