Page 41 - Force 10

Conditions:

2) When the distance between their centres is changed keeping their masses constant.
a) If the distance between their centre is halved, keeping their masses same.

Ans: Case I m 1 m

st
let the mass of 1 object be m kg, 2
1
nd
the mass of 2 object be m kg,
2
distance between their centres be d m.
× 2 …… (i) d
1
According to the Newton’s law of gravitation: F = G 2
1

Case II A B
st
let the mass of 1 object ( m ) = m kg,
1 1
nd
the mass of 2 object (m ) = m kg, m 1 m 2
2
2
distance between their centres be d/2 m.
× 2 …… (ii)
1
According to the Newton’s law of gravitation: F = G 2
2

× 2 d/2
1
= G A B
( ) 2
2
× 2
1
= 4 × G
2

= 4 F 1

∴ F = 4 F 1
2

Hence, the new gravitational force is increased by 4 times than the initial force.