1. no
2. yes
3. depends on the mass of the planet
4. we can't say anything
Three equal masses of \(m\) kg each are fixed at the vertices of an equilateral triangle \(ABC.\) What is the force acting on a mass \(2m\) placed at the centroid \(G\) of the triangle?
(Take \(AG=BG=CG=1\) m.)
1. \(Gm^2(\hat{i}+\hat{j})\)
2. \(Gm^2(\hat{i}-\hat{j})\)
3. zero
4. \(2Gm^2(\hat{i}+\hat{j})\)
Three equal masses of m kg each are fixed at the vertices of an equilateral triangle ABC. What is the force acting on a mass 2m placed at the centroid G of the triangle if the mass at the vertex A is doubled? Take AG = BG = CG = 1 m.
1. \(Gm^{2} \left(\hat{i} + \hat{j}\right)\)
2. \(Gm^{2} \left(\hat{i} - \hat{j}\right)\)
3. 0
4. \(2Gm^{2} \hat{j}\)
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:
1. | \(\left(\dfrac{3 {GM}}{5 {R}}\right)^{1 / 2}\) | 2. | \(\left(\dfrac{2 {GM}}{5 {R}}\right)^{1 / 2}\) |
3. | \(\left(\dfrac{3 {GM}}{2 {R}}\right)^{1 / 2}\) | 4. | \(\left(\dfrac{5 {GM}}{3 {R}}\right)^{1 / 2}\) |
The planet Mars has two moons, Phobos and Delmos. Phobos has a period of \(7\) hours, \(39\) minutes and an orbital radius of km. The mass of mars is:
1.
2.
3.
4.
You are given the following data: \(g = 9.81~ \text{m/s}^{2}\), \(R_{E} = 6 . 37 \times 10^{6}~\text m\), the distance to the moon, \(R = 3 . 84 \times 10^{8}~\text m\) and the time period of the moon’s revolution is 27.3 days. Mass of the Earth \(M_{E}\) in two different ways is:
1. \(5 . 97 \times 10^{24} ~ \text{kg and }6 . 02 \times 10^{24} \text{ kg}\)
2. \(5 . 97 \times 10^{24} \text{ kg and } 6 . 02 \times 10^{23} \text{ kg}\)
3. \(5 . 97 \times 10^{23} ~ \text{kg and }6 . 02 \times 10^{24} \text{ kg}\)
4. \(5 . 97 \times 10^{23} \text{ kg and } 6 . 02 \times 10^{23} \text{ kg}\)
Constant \(k = 10^{- 13} ~ \text s^{2}~ \text m^{- 3}\) in days and kilometres is?
1. \(10^{- 13} ~ \text d^{2} ~\text{km}^{- 3}\)
2. \(1 . 33 \times 10^{14} \text{ dkm}^{- 3}\)
3. \(10^{- 13} ~ \text d^{2} ~\text {km}\)
4. \(1 . 33 \times 10^{- 14} \text{ d}^{2} \text{ km}^{- 3}\)
A \(400\) kg satellite is in a circular orbit of radius \(2R_E\) (where \(R_E\) is the radius of the earth) about the Earth. How much energy is required to transfer it to a circular orbit of radius \(4R_E\)\(?\)
(Given \(R_E=6.4\times10^{6}\) m)
1. \(3.13\times10^{9}\) J
2. \(3.13\times10^{10}\) J
3. \(4.13\times10^{9}\) J
4. \(4.13\times10^{8}\) J