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___________ \(cm\)

A massless spring gets elongated by amount \(x_1\) under a tension of 5 N . Its elongation is \(x_2\) under the tension of 7 N . For the elongation of \(\left(5 x_1-2 x_2\right)\), the tension in the spring will be,

Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance \(( R / 2)\) from the earth's centre, where \('R'\) is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period

A sample of radioactive material \(A\), that has an activity of \(10\, mCi\, (1\, Ci = 3.7 \times 10^{10}\, decays/s)\), has twice the number of nuclei as another sample of different radioactive material \(B\) which has an activity of \(20\, mCi\). The correct choices for half-lives of \(A\) and \(B\) would then be respectively

Correct formula for height of a satellite from earths surface is _______.

The bulk modulus of a liquid is \(3 \times 10^{10}\, Nm ^{-2}\). The pressure required to reduce the volume of liquid by \(2 \%\) is  ........ \(\times 10^{8}\; Nm ^{-2}\)

Keeping the significant figures in view, the sum of the physical quantities \(52.01 m, 153.2 m\) and 0.123 m is :

In the wave equation \(y =0.5 \sin \frac{2 \pi}{\lambda}(400 t - x )\,m\)  the velocity of the wave will be ......... \(m / s\)

A particle moves in \(\mathrm{x}-\mathrm{y}\) plane under the influence of a force \(\vec{F}\) such that its linear momentum is \(\vec{P}(t)=\hat{i} \cos (k t)-\hat{j} \sin (k t)\). If \(k\) is constant, the angle between \(\overrightarrow{\mathrm{F}}\) and \(\overrightarrow{\mathrm{P}}\) will be _______.