Two A body starts from rest from a point distant r0 from the centre of the earth. It reaches the surface of the earth…..

Q: Two A body starts from rest from a point distant r0 from the centre of the earth. It reaches the surface of the earth whose radius is R. The velocity acquired by the body is

(a) $\displaystyle 2 G M \sqrt{\frac{1}{R}-\frac{1}{r_0}}$

(b) $\displaystyle \sqrt{2 G M(\frac{1}{R}-\frac{1}{r_0})}$

(c) $\displaystyle G M \sqrt{\frac{1}{R}-\frac{1}{r_0}}$

(d) $\displaystyle \sqrt{G M(\frac{1}{R}-\frac{1}{r_0})}$

Ans: (b)

The radius of a planet is R. A satellite revolves around it in a circle of radius r with angular velocity …..

Q: The radius of a planet is R. A satellite revolves around it in a circle of radius r with angular velocity ω0. The acceleration due to the gravity on planet’s surface is

(a) $\displaystyle \frac{r^3 \omega_0}{R}$

(b) $\displaystyle \frac{r^3 \omega_0^3}{R^2}$

(c) $\displaystyle \frac{r^3 \omega_0^3}{R}$

(d) $\displaystyle \frac{r^3 \omega_0^2}{R^2}$

Ans: (d)

A geostationary satellite orbits around the earth in a circular orbit of radius 36000 km. Then……

Q: A geostationary satellite orbits around the earth in a circular orbit of radius 36000 km. Then, the time period of a spy satellite orbiting a few 100 km above the earth’s surface (Rearth = 6400km) will approximately be

(a) 1/2 h

(b) 1 h

(c) 2 h

(d) 4 h

Ans: (c)

A body is released from a point of distance R’ from the centre of earth. Its velocity at the time of….

Q: A body is released from a point of distance R’ from the centre of earth. Its velocity at the time of striking the earth will be (R’ > Re)
(a) $\displaystyle \sqrt{2 g R_e}$

(b) $\displaystyle \sqrt{ g R_e}$

(c) $\displaystyle \sqrt{2 g (R' - R_e) }$

(d) $\displaystyle \sqrt{2 g R_e (1- \frac{R_e}{R'})}$

Ans: (d)

A uniform ring of mass m and radius r is placed directly above a uniform sphere of mass M and of equal radius. …

Q: A uniform ring of mass m and radius r is placed directly above a uniform sphere of mass M and of equal radius. The centre of the ring is directly above the centre of the sphere at a distance as shown in the figure. The gravitational force exerted by the sphere on the ring will be

(a) $\displaystyle \frac{G M m}{8 r^2}$

(b) $\displaystyle \frac{G M m}{4 r^2}$

(c) $\displaystyle \sqrt3 \frac{G M m}{8 r^2}$

(d) $\displaystyle \frac{G M m}{8 r^3 \sqrt3}$

Ans: (c)