Question

Assertion (A): If both the mass and radius of the earth decreases by 1%,

the value of acceleration due to gravity will increase by 2%.

Reason (R): g= GMm/R2
​

Answer 1

Explanation:

The acceleration due to gravity is: g=

R

2

GM

The new value of g would be: g

′

=

(0.99R)

2

G(0.99M)

≃1.01

R

2

GM

=1.01g

Thus,g would increase by about 1%.The new escape velocity would be:

V

e

′

=

0.99R

2×0.99M×G

=

R

2MG

=V

e

Thus,the escape velocity will remain unchanged.The potential energy of a body of mass m on earth's surface would be

−

(0.99R)

GM(0.99M)

=−

R

GmM

Thus,the potential energy will also remain unchanged.Hence,the correct choices are (b) and (d).