Assertion: When distance between two bodies is doubled and also mass of each body is doubled, gravitational force between them remains the same. Reason: According to Newton’s law of gravitation, force is directly proportional to product of the mass of bodies and inversely proportional to the square of the distance between them.

Question

Assertion: When distance between two bodies is doubled and also mass of each body is doubled, gravitational force between them remains the same. Reason: According to Newton’s law of gravitation, force is directly proportional to product of the mass of bodies and inversely proportional to the square of the distance between them. (A) If both assertion and reason are true and reason is the correct explanation of assertion (B) If both assertion and reason are true but reason is not the correct explanation of assertion (C) If assertion is true but reason is false (D) If both assertion and reason are false

Tardigrade Admin · Accepted Answer

According to Newtons law of gravitation, F = (Gm1m2/r2). When m1, m2 and r all are doubled, F= (G(2m1)(2m2)/(2r)2) = (Gm1m2/r2), i.e. F remains the same.

If both assertion and reason are true and reason is the correct explanation of assertion

If both assertion and reason are true but reason is not the correct explanation of assertion

If assertion is true but reason is false

If both assertion and reason are false

According to Newtons law of gravitation, F=r2Gm1​m2​​. When m1​, m2​ and r all are doubled, F=(2r)2G(2m1​)(2m2​)​=r2Gm1​m2​​, i.e. F remains the same.

According to Newtons law of gravitation, $F = \frac{G m _{1} m _{2}}{r ^{2}}$ . When $m_{1}$ , $m_{2}$ and $r$ all are doubled, $F = \frac{G ( 2 m _{1} ) ( 2 m _{2} )}{( 2 r ) ^{2}} = \frac{G m _{1} m _{2}}{r ^{2}}$ , i.e. $F$ remains the same.