Question

If the charge on a body is increased by $2C$, the energy stored in it increases by $21$%. The original charge on the body in coulombs is :

• A. $10$
• B. $20$
• C. $30$
• D. $40$

Answer 1

The correct option is B $20$

We know energy stored $E=\frac{Q^2}{2c}$
When Q is increased by 2c
energy stored increases by$21$%

$\Rightarrow (E+\frac{21}{100}E)=\frac{(Q+2{)}^2}{2c}$

$\frac{Q^2}{2c}(1+0.21)=\frac{(Q+2{)}^2}{2c}$

$Q^2=\frac{(Q+2{)}^2}{1.21}$

$Q=\frac{Q+2}{1.1}$

$\Rightarrow 1.1Q=Q+2$

$\Rightarrow 0.1Q=2$

$\Rightarrow Q=20$