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 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

Numerical

(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)