The magnitude of gravitational potential energy of a body at a distance ' $R$ ' from the centre of the earth is ' E '. Its weight at a distance ' 1.5 R ' from the centre of the earth is

The de-Broglie wavelength of a neutron at $27^{\circ} \mathrm{C}$ is ' $\lambda_0$ '. What will be its wavelength at $927^{\circ} \mathrm{C}$ ?

Earth is assumed to be a charged conducting sphere having volume V and surface area A . The capacitance of the earth in free space is ( $\varepsilon_0=$ permittivity of free space)

A particle performing linear S.H.M. has period 8 seconds. At time $\mathrm{t}=0$, it is in the mean position. The ratio of the distances travelled by the particle in the $1^{\text {st }}$ and $2^{\text {nd }}$ second is $\left(\cos 45^{\circ}=1 / \sqrt{2}\right)$