A mass of \(50\, {kg}\) is placed at the centre of a uniform spherical shell of mass \(100\, {kg}\) and radius \(50 \,{m}\). If the gravitational potential at a point, \(25\, {m}\) from the centre is \({V} \,{kg} / {m} .\) The value of \({V}\) is

A solid ball of radius \(R\) has a charge density \(\rho \) given by \(\rho  = {\rho _0}\left( {1 - \frac{r}{R}} \right)\) for \(0 \leq r \leq R\). The electric field outside the ball is

A simple pendulum of string length 30 cm performs 20 oscillations in 10s. The length of the string required for the pendulum to perform 40 oscillations in the same time duration is ___________ cm. [Assume that the mass of the pendulum remains same.]

In a system two particles of masses \(m_1=3 \mathrm{~kg}\) and \(\mathrm{m}_2=2 \mathrm{~kg}\) are placed at certain distance from each other. The particle of mass \(m_1\) is moved towards the center of mass of the system through a distance \(2 \mathrm{~cm}\). In order to keep the center of mass of the system at the original position, the particle of mass \(\mathrm{m}_2\) should move towards the center of mass by the distance _______\(\mathrm{cm}\).

The maximum percentage error in the measurment of density of a wire is [Given, mass of wire \(=(0.60 \pm 0.003) \mathrm{g}\)
radius of wire \(=(0.50 \pm 0.01) \mathrm{cm}\)
length of wire \(=(10.00 \pm 0.05) \mathrm{cm}]\)

When a current of \(5\ mA\) is passed through a galvanometer having a coil of resistance \(15\ \Omega\), it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into to voltmeter of range \(0 - 10\ V\) is

The velocity of a particle is \(v = v _{0}+ gt + Ft ^{2}\). Its position is \(x=0\) at \(t=0\); then its displacement after time \(( t =1)\) is :

A copper wire is stretched to make it \(0.5\%\) longer. The percentage change in its electric resistance if its volume remains unchanged is ................ \(\%\)

A singly ionized magnesium atom \((A=24)\) ion is accelerated to kinetic energy \(5\,keV\) and is projected perpendicularly into a magnetic field \(B\) of the magnitude \(0.5\,T\). The radius of path formed will be___________ \(cm\)