Two massless springs with spring constants \(2\,k\) and \(9\,k\), carry \(50\, g\) and \(100 \,g\) masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be

Two radioactive elements \(A\) and \(B\) initially have same number of atoms. The half life of \(A\) is same as the average life of \(B\). If \(\lambda_A\) and \(\lambda_B\) are decay constants of \(A\) and \(B\) respectively, then choose the correct relation from the given options.

An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging from the analyzer is measured as \(100\) Lumens. Now, if the analyzer is rotated around the horizontal axis (direction of light) by \(30^{\circ}\) in clockwise direction, the intensity of emerging light will be .......... Lumens.

A car of \(800 \mathrm{~kg}\) is taking turn on a banked road of radius \(300 \mathrm{~m}\) and angle of banking \(30^{\circ}\). If coefficient of static friction is \(0.2\) then the maximum speed with which car can negotiate the turn safely which? \(\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sqrt{3}=1.73\right)\)

Wax is coated on the inner wall of a capillary tube and the tube is then dipped in water. Then, compared to the unwaxed capillary, the angle of contact \(\theta \) and the height \(h\) upto which water rises change. These changes are

A gas is compressed adiabatically, which one of the following statement is NOT true.

The distance between object and its two times magnified real image as produced by a convex lens is \(45 \mathrm{~cm}\). The focal length of the lens used is _______ \(\mathrm{cm}\).

The identical spheres each of mass \(2 \mathrm{M}\) are placed at the corners of a right angled triangle with mutually perpendicular sides equal to \(4 \mathrm{~m}\) each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is \(\frac{4 \sqrt{2}}{x}\), where the value of \(x\) is _______.

A big drop is formed by coalescing \(1000\) small identical drops of water. If \(E_1\) be the total surface energy of \(1000\) small drops of water and \(E_2\) be the surface energy of single big drop of water, the \(E_1\) : \(\mathrm{E}_2\) is \(\mathrm{x}: 1\) where \(x\) = _____.

In a photoelectric effect experiment, the graph of stopping potential \(V\) versus reciprocal of wavelength obtained is shown in the figure. As the intensity of incident radiation is increased