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BITSAT 2023Paper 1

Exam: BITSAT
Year: 2023
Paper: Paper 1
Subject: Physics
Chapter: Gravitation

BITSAT 2023 · Paper 1 · Physics · Gravitation

Two planets A and B of radii R and 1.5 R have densities and / 2...

Two planets

A

and

B

of radii

R

and

1.5 R

have densities

\rho

and

\rho / 2

respectively. The ratio of acceleration due to gravity at the surface of

B

to A is :

Options

A $2: 3$
B $2: 1$
C $3: 4$
D $4: 3$

Correct answer

C. $3: 4$

Step-by-step solution

Acceleration due to gravity,

\mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^2}=\frac{4}{3} \pi \mathrm{G} \rho \mathrm{R}

\therefore \frac{g_2}{g_1}=\frac{\rho_2}{\rho_1} \times \frac{R_2}{R_1}=\frac{1}{2} \times 1.5=\frac{3}{4}

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