EASY

JEE Main/Advance

IMPORTANT

Earn 100

The minimum and maximum distances of a satellite from the centre of the Earth are $2 R$ and $4 R$ respectively, where, $R$ is the radius of Earth and $M$ is the mass of the Earth. Radius of curvature at the point of minimum distance is $\frac{α R}{3}$ , then the value of $α$ is,

50% studentsanswered this correctly

Important Questions on Gravitation

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Physics>Chapter 11 - Gravitation>Exercise-4>Q 1

A satellite of mass

m

is in an elliptical orbit around Earth of mass

M (M ≫ m)

. The speed of the satellite at its nearest point to the Earth is

\sqrt{\frac{6 GM}{5 R}}

, where

R =

perigee(closest distance to the Earth). It is desired to transfer this satellite into a circular orbit around the Earth of radius equal its largest distance from the Earth. If the increase in its speed to be imparted at the apogee (farthest point on the elliptical orbit) is of the form

\sqrt{\frac{GM}{R}} [\sqrt{\frac{a}{3}} - \sqrt{\frac{b}{15}}]

. Find

a + b

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Physics>Chapter 11 - Gravitation>Exercise-4>Q 2

A body is launched from the Earth's surface at an angle

α = 30 °

to the horizontal with speed

v_{0} = \sqrt{\frac{1.5 GM}{R}}

. Neglecting air resistance and Earth's rotation, if the height to which the body will rise is

(\frac{\sqrt{7}}{2} + β) R

, then find value of

β

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Physics>Chapter 11 - Gravitation>Exercise-4>Q 3

Distance between the centres of two starts is

10 a

. The masses of these stars are

M

and

16 M

and their radius

a

and

2 a

respectively. A body of mass

m

is fired straight from the surface of the larger star towards the surface of the smaller star. Now if its minimum initial speed to reach the surface of the smaller star in terms of

G, M

and

a

\frac{3}{2} \sqrt{\frac{β G M}{a}}

, then find value of

β

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Physics>Chapter 11 - Gravitation>Exercise-4>Q 4

If the potential energy of a system of four particles placed at the vertices of a square of side

l

\frac{- 5.41 {Gm}^{α}}{l}

and the potential at the centre of the square is

\frac{- 4 \sqrt{β} Gm}{l}

, then find

α + β

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Physics>Chapter 11 - Gravitation>Exercise-4>Q 5

A satellite of mass

M_{s}

is orbiting the Earth in a circular orbit of radius

R_{s}

. It starts losing energy slowly at a constant rate

C

due to friction. If

M_{e}

and

R_{e}

denote the mass and radius of the Earth respectively, show that the satellite falls on the Earth in a limit time

t

given by

t = \frac{G M_{s} M_{e}}{2 C} (\frac{1}{R_{e}} - \frac{1}{R_{s}})

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Physics>Chapter 11 - Gravitation>Exercise-4>Q 6

A rocket starts vertically upwards with speed

v_{0} .

If its speed

v

at a height

h

is given by

v_{0}^{2} - v^{2} = [\frac{(β g h)}{(1 + \frac{h}{R})}]

, then find value of

β .

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Physics>Chapter 11 - Gravitation>Exercise-4>Q 7

A cord of length

64 m

is used to connect a

100 kg

astronaut to spaceship whose mass is much larger than that of the astronaut. If the value of the tension in the cord is

x \times 10^{- 2} N

, then find value of

x

. Assume that the spaceship is orbiting near Earth surface also assume that the spaceship and the astronaut fall on a straight line from the Earth centre. The radius of the Earth is

6400 km

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Physics>Chapter 11 - Gravitation>Exercise-4>Q 8

A remote sensing satellite is revolving in an orbit of radius

x

on the equator of Earth. If the area on Earth surface in which satellite can not send message is

(β - \frac{\sqrt{x^{2} - R^{2}}}{x}) 4 π R^{2}

, then find

β

The minimum and maximum distances of a satellite from the centre of the Earth are 2R and 4R respectively, where, R is the radius of Earth and M is the mass of the Earth. Radius of curvature at the point of minimum distance isαR3 , then the value of α is,

Important Questions on Gravitation

Learn and Prepare for any exam you want !

The minimum and maximum distances of a satellite from the centre of the Earth are $2 R$ and $4 R$ respectively, where, $R$ is the radius of Earth and $M$ is the mass of the Earth. Radius of curvature at the point of minimum distance is $\frac{α R}{3}$ , then the value of $α$ is,