A parallel plate capacitor of capacitance \(90\ pF\) is connected to a battery of \(emf\) \(20\ V\). If a dielectric material of dielectric constant \(K = \frac{5}{3}\) is inserted between the plates, the magnitude of the induced charge will be.......\(n \) \(C\)

Given below are two statements: One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one. Reason \(R:\) Capacitance of metallic spheres depend on the radii of spheres. In the light of the above statements, choose the correct answer from the options given below.

The height of any point \(P\) above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point \(P\) will be : (Given \(g=\) acceleration due to gravity at the surface of earth)

An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?

A fly wheel is accelerated uniformly from rest and rotates through \(5 \,rad\) in the first second. The angle rotated by the fly wheel in the next second, will be.........\(rad\)

The masses and radii of the earth and moon are \(\left({M}_{1}, {R}_{1}\right)\) and \(\left({M}_{2}, {R}_{2}\right)\) respectively. Their centres are at a distance ' \({r}\) ' apart. Find the minimum escape velocity for a particle of mass ' \({m}\) ' to be projected from the middle of these two masses:

An unpolarized light of intensity \(I_o\) passes through polarizer and then through a certain optically active solution and finally it goes to analyser. If the angle between analyser and polariser is \(0°\) and intensity of light emerged from analyser is \(\dfrac{3}{8}I_o\), the angle of rotation of the light by the solution with respect to analyser is _______ degrees.

In a spring gun having spring constant \(100\, {N} / {m}\) a small ball \('B'\) of mass \(100\, {g}\) is put in its barrel (as shown in figure) by compressing the spring through \(0.05\, {m}\). There should be a box placed at a distance \('d'\) on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of \(2\, {m}\) above the ground. The value of \(d\) is \(....{m} .\) \(\left(g=10\, {m} / {s}^{2}\right)\)

A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample is _______.

Four \(NOR\) gates are connected as shown in figure. The truth table for the given figure is :