Page 40 - Force 10

Conditions:

1) When mass is changed keeping the distance between them constant.

a) If the mass of one object is doubled, keeping their distance same.

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

Case II

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

2 × 2 d
1
= G
2
× 2 A B
1
= 2 × G
2

= 2 F 1

∴ F = 2 F 1
2
Hence, the new gravitational force is increased by 2 times than the initial force.