Question

A force of $25\text{N}$ is applied individually on two objects $A$ and $B$ such that the acceleration of $A$ and $B$ is in the ratio 4 : 3. If the force is increased to $30\text{N}$, then the difference in the ratios of new and earlier accelerations is:

Answer 1

Case - I
Acceleration in $A$ object, $a_1=\frac{25}{m_1}$
Acceleration in $B$ object, $a_2=\frac{25}{m_2}$
$\therefore \frac{a_1}{a_2}=\frac{\frac{25}{m_1}}{\frac{25}{m_2}}=\frac{m_2}{m_1}=\frac{4}{3}$

Case - II
Acceleration in $A$ object, $A_1=\frac{30}{m_1}$
Acceleration in $B$ object, $A_2=\frac{30}{m_2}$
$\therefore \frac{a_1}{a_2}=\frac{\frac{25}{m_1}}{\frac{25}{m_2}}=\frac{m_2}{m_1}=\frac{4}{3}$

$\therefore$ The difference in new and earlier acceleration
$\frac{4}{3}-\frac{4}{3}=0$