- 1(current)
Q. No.(\(M=\) mass of the earth, \(G=\) gravitational constant):
| 1. | \(\dfrac{GMm}{r}\) | 2. | \(\dfrac{-GMm}{r}\) |
| 3. | \(\dfrac{GM}{r}\) | 4. | \(\dfrac{-GM}{r}\) |
Given below are two statements:
| Assertion (A): | When a body is raised from the surface of the earth, its potential energy increases. |
| Reason (R): | Potential energy of a body on the surface of the earth is zero. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
1. \({\dfrac{1}{3}{mgR}_{e}}\)
2. \({\dfrac{1}{6}{mgR}_{e}}\)
3. \({\dfrac{1}{2}{mgR}_{e}}\)
4. \({\dfrac{1}{4}{mgR}_{e}}\)
(\(R\) is the radius of the planet)
| 1. | \(-\dfrac{GMm}{2R}\) | 2. | \(-\dfrac{GMm}{R}\) |
| 3. | \(-\dfrac{3GMm}{2R}\) | 4. | \(-\dfrac{3GMm}{R}\) |
1. \(\dfrac{3}{2}mgR\)
2. \(mgR\)
3. \(2mgR\)
4. \(\dfrac{1}{2}mgR\)
The potential energy of a system of four particles placed at the vertices of a square of side \(l\) (as shown in the figure below) and the potential at the centre of the square, respectively, are:
1. \(- 5 . 41 \dfrac{Gm^{2}}{l}\) and \(0\)
2. \(0\) and \(- 5 . 41 \dfrac{Gm^{2}}{l}\)
3. \(- 5 . 41 \dfrac{Gm^{2}}{l}\) and \(- 4 \sqrt{2} \dfrac{Gm}{l}\)
4. \(0\) and \(0\)
Two uniform solid spheres of equal radii \({R},\) but mass \({M}\) and \(4M\) have a centre to centre separation \(6R,\) as shown in the figure. The two spheres are held fixed. A projectile of mass \(m\) is projected from the surface of the sphere of mass \(M\) directly towards the centre of the second sphere. The expression for the minimum speed \(v\) of the projectile so that it reaches the surface of the second sphere is:
2. \(\left(\dfrac{2 {GM}}{5 {R}}\right)^{1 / 2}\)
3. \(\left(\dfrac{3 {GM}}{2 {R}}\right)^{1 / 2}\)
4. \(\left(\dfrac{5 {GM}}{3 {R}}\right)^{1 / 2}\)
Assuming that the gravitational potential energy of an object at infinity is zero, the change in potential energy (final - initial) of an object of mass \(m\) when taken to a height \(h\) from the surface of the earth (of radius \(R\) and mass \(M\)), is given by:
| 1. | \(-\frac{GMm}{R+h}\) | 2. | \(\frac{GMmh}{R(R+h)}\) |
| 3. | \(mgh\) | 4. | \(\frac{GMm}{R+h}\) |
| 1. | \(U > mgh\) |
| 2. | \(U < mgh\) |
| 3. | \(U = mgh\) |
| 4. | any of the above may be true depending on the value of \(h,\) considered relative to the radius of the earth. |
- 1(current)
Q. No.
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