Centripetal Force

Q. A uniformly charged thin spherical shell of radius $R$ carries a uniform surface charge density of $\sigma$ per unit area. It is made of two hemispherical shells, held together by pressing them with a force $F$ (see the figure). $F$ is proportional to

1. $\frac{1}{{ϵ}_0}{\sigma }^2{R}^2$
2. $\frac{1}{{ϵ}_0}{\sigma }^{2}R$
3. $\frac{1}{{ϵ}_0}\frac{{\sigma }^2}{R}$
4. $\frac{1}{{ϵ}_0}\frac{{\sigma }^2}{R^2}$

Q. If a particle of mass m is moving in a horizontal circle of radius r with a centripetal force (-$\frac{k}{r^2}$) , the total energy is

1. - $\frac{k}{2r}$
2. - $\frac{k}{r}$
3. - $\frac{2k}{r}$
4. - $\frac{4k}{r}$

Q.

A car moving on a horizontal road may be thrown out of the road in taking a turn

1. By the gravitational force

2. Due to lack of sufficient centripetal force

3. Due to rolling frictional force between tyre and road

4. Due to the reaction of the ground

Q. A uniformly charged thin spherical shell of radius $R$ carries a uniform surface charge density of $\sigma$ per unit area. It is made of two hemispherical shells, held together by pressing them with a force $F$ (see the figure). $F$ is proportional to

1. $\frac{1}{{ϵ}_0}{\sigma }^{2}R$
2. $\frac{1}{{ϵ}_0}\frac{{\sigma }^2}{R^2}$
3. $\frac{1}{{ϵ}_0}\frac{{\sigma }^2}{R}$
4. $\frac{1}{{ϵ}_0}{\sigma }^2{R}^2$