The particles A and B of mass m each are sepa | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Since particle $C$ is moved without any acceleration,the change in kinetic energy is zero,$\Delta K.E. = 0$.By the work-energy theorem,the work do

Vedclass · Accepted Answer

$\frac{2 G M m}{r}$

Vedclass · Answer

(B) Since particle $C$ is moved without any acceleration,the change in kinetic energy is zero,$\Delta K.E. = 0$.By the work-energy theorem,the work done by an external agent plus the work done by gravitational forces is zero: $W_{	ext{ext}} + W_{	ext{grav}} = 0$.Therefore,$W_{	ext{ext}} = -W_{	ext{grav}} = \Delta U = U_f - U_i$.The gravitational potential energy of the system involving particle $C$ is $U = -\frac{GMm}{r_A} - \frac{GMm}{r_B}$,where $r_A$ and $r_B$ are the distances of $C$ from $A$ and $B$ respectively.Initial position: $C$ is at the midpoint,so $r_A = r/2$ and $r_B = r/2$.$U_i = -\frac{GMm}{r/2} - \frac{GMm}{r/2} = -\frac{2GMm}{r} - \frac{2GMm}{r} = -\frac{4GMm}{r}$.Final position: $C$ is at a point equidistant $r$ from $A$ and $B$,so $r_A = r$ and $r_B = r$.$U_f = -\frac{GMm}{r} - \frac{GMm}{r} = -\frac{2GMm}{r}$.Work done $W_{	ext{ext}} = U_f - U_i = -\frac{2GMm}{r} - (-\frac{4GMm}{r}) = \frac{2GMm}{r}$.

Similar Questions

If $W_1, W_2$ and $W_3$ represent the work done in moving a particle from $A$ to $B$ along three different paths $1, 2$ and $3$ (as shown in the figure) in the gravitational field of the point mass '$m$',find the correct relation between '$W_1$','$W_2$' and '$W_3$'.

Which of the following most closely depicts the correct variation of the gravitational potential $V(r)$ due to a large planet of radius $R$ and uniform mass density? (figures are not drawn to scale)

If $V$ is the gravitational potential due to a sphere of uniform density on its surface,then its value at the center of the sphere will be:

The gravitational field in a region is given by the equation $E = (5\hat{i} + 12\hat{j}) \text{ N/kg}$. If a particle of mass $2 \text{ kg}$ is moved from the origin $(0, 0)$ to the point $(12 \text{ m}, 5 \text{ m})$ in this region, the change in gravitational potential energy is: (in $\text{ J}$)

The masses $m$ in figures $(A)$ and $(B)$ are identical. The gravitational potential energy in the two cases are $U_A$ and $U_B$. Then

Vedclass Test Series

Exam Paper Generator

Online Exam Module