Question

A body of mass M and charge q is suspended from a string. When slightly displaced, it oscillates with period T. If a uniform electric field acts vertically downwards, then the new time period will be:

• A. $T^{\prime }=T$
• B. $T^{\prime }<T$
• C. $T^{\prime }>T$
• D. cannot be predicted

Answer 1

The correct option is B $T^{\prime }<T$

Here, $T=2\pi \sqrt{\frac{l}{g}}$
When electric field is applied downward the effective acceleration will increase i,e $g^{\prime }=g+\frac{qE}{M}$
Thus, $T^{\prime }=2\pi \sqrt{\frac{l}{g+qE/M}}$
Hence, $T^{\prime }<T$