Question

If same force acts on a body, what will happen ton acceleration of the object when its (a) mass is doubled (b) Mass is made 1/4th? Also determine the ratio of acceleration in the above two cases.

Answer 1

Let F be the force applied on object of mass M
then, $F=Ma$or $a=\frac{F}{M}\left(a=accelerationofobject\right)$

(a) If mass is doubled, $a_1=\frac{F}{2M}$

(b) If mass is made 1/4 th $a_2=\frac{F}{{\displaystyle \frac{M}{4}}}=\frac{4F}{M}$

$\frac{a_1}{a_2}=\frac{{\displaystyle \frac{F}{2M}}}{{\displaystyle \frac{4F}{M}}}=\frac{F\times M}{2M\times 4F}=\frac{1}{8}$

Ration of two accelerations is 1:8