A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q . If it acquires a speed ν when it has fallen…

Question

A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q . If it acquires a speed &#957; when it has fallen through a vertical height y (see figure), then (assume the remaining portion to be spherical)

Aicharya · Accepted Answer

By using total energy conservation &#916; KE + ( &#916; PE ) electo &#160; + ( &#916; PE ) gravitation &#160; = 0 1 2 m V 2 + k Q q R + y - k Q q R + ( - m g y ) = 0 1 2 m V 2 = m g y + k Q q 1 R - 1 R + y ; &#160; &#160; V 2 = 2 g y + 2 k Q q m y R ( R + y ) V 2 = 2 y q Q 4 &#960; &#949; 0 R ( R + y ) m + g

A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point…

Solution