If a planet was suddenly stopped in its orbit supposed to be circular, then it would fall onto the sun in a time that …..

Q: If a planet was suddenly stopped in its orbit supposed to be circular, then it would fall onto the sun in a time that is n times the period of the planet’s revolution. Where n is

(a) √3/8

(b) 1/8

(c) √2/8

(d) 1/4

Ans: (c)

With what minimum speed should m be projected from point C in presence of two fixed masses M …..

Q: With what minimum speed should m be projected from point C in presence of two fixed masses M each at A and B as shown in the figure such that mass m should escape the gravitational attraction of A and B?

Numerical

(a) \displaystyle \sqrt{\frac{2GM}{R}}

(b) \displaystyle \sqrt{\frac{2\sqrt2 GM}{R}}

(c) \displaystyle 2\sqrt{\frac{GM}{R}}

(d) \displaystyle 2\sqrt2 \sqrt{\frac{GM}{R}}

Ans: (b)

The density of the core of a planet is ρ1 and that of the outer shell is ρ2, the radii of the core and that of the planet….

Q: The density of the core of a planet is ρ1 and that of the outer shell is ρ2, the radii of the core and that of the planet are R and 2R respectively. The acceleration due to gravity at the surface of the planet is same as at a depth R. Find the ratio of ρ12

Numerical

(a) 3/7

(b) 7/4

(c) 4/7

(d) 7/3

Ans: (d)

A tunnel is dug along the diameter of the earth. There is a particle of mass m at the centre of the tunnel…..

Q: A tunnel is dug along the diameter of the earth. There is a particle of mass m at the centre of the tunnel. Find the minimum velocity given to the particle so that is just reaches to the surface of the earth. (R = radius of earth)

(a) \displaystyle \sqrt{\frac{GM}{R}}

(b) \displaystyle \sqrt{\frac{GM}{2R}}

(c) \displaystyle \sqrt{\frac{2GM}{R}}

(d) it will reach with the help of negligible velocity

Ans: (a)