1. | \(11.2\sqrt2~\text{km/s}\) | 2. | zero |
3. | \(11.2~\text{km/s}\) | 4. | \(11.2\sqrt3~\text{km/s}\) |
1. | \(\dfrac{\pi RG}{12g}\) | 2. | \(\dfrac{3\pi R}{4gG}\) |
3. | \(\dfrac{3g}{4\pi RG}\) | 4. | \(\dfrac{4\pi G}{3gR}\) |
1. | \(+\dfrac K2\) | 2. | \(-\dfrac{K}{2}\) |
3. | \(-\dfrac{K}{4}\) | 4. | \(+\dfrac K4\)
|
Two planets orbit a star in circular paths with radii \(R\) and \(4R,\) respectively. At a specific time, the two planets and the star are aligned in a straight line. If the orbital period of the planet closest to the star is \(T,\) what is the minimum time after which the star and the planets will again be aligned in a straight line?
1. | \((4)^2T\) | 2. | \((4)^{\frac13}T\) |
3. | \(2T\) | 4. | \(8T\) |
Assuming the earth to be a sphere of uniform density, its acceleration due to gravity acting on a body:
1. | increases with increasing altitude. |
2. | increases with increasing depth. |
3. | is independent of the mass of the earth. |
4. | is independent of the mass of the body. |
List-I | List-II | ||
(a) | Gravitational constant (\(G\)) | (i) | \([{L}^2 {~T}^{-2}] \) |
(b) | Gravitational potential energy | (ii) | \([{M}^{-1} {~L}^3 {~T}^{-2}] \) |
(c) | Gravitational potential | (iii) | \([{LT}^{-2}] \) |
(d) | Gravitational intensity | (iv) | \([{ML}^2 {~T}^{-2}]\) |
(a) | (b) | (c) | (d) | |
1. | (iv) | (ii) | (i) | (iii) |
2. | (ii) | (i) | (iv) | (iii) |
3. | (ii) | (iv) | (i) | (iii) |
4. | (ii) | (iv) | (iii) | (i) |
1. | \(180 ~\text{N/kg}\) | 2. | \(0.05 ~\text{N/kg}\) |
3. | \(50 ~\text{N/kg}\) | 4. | \(20 ~\text{N/kg}\) |