A stone is dropped from the top of a building. When it crosses a point \(5\, m\) below the top, another stone starts to fall from a point \(25\, m\) below the top. Both stones reach the bottom of building simultaneously. The height of the building is ..... \(m\).

Three capacitors each of \(4\,\,\mu F\)  are to be connected in such a way that the effective capacitance is \(6\,\,\mu F.\)  This can be done by connecting thern

The region between \(y = 0\) and \(y = d\) contains a magnetic field \(\vec B = B\hat z\) A particle of mass \(m\) and charge \(q\) enters the region with a velocity \(\vec v = v\hat i\). If \(d = \frac{{mv}}{{2qB}}\) , the acceleration of the charged particle at the point of its emergence at the other side is

A uniform disc of mass \(0.5\,kg\) and radius \(r\) is projected with velocity \(18\,m / s\) at \(t =0\,s\) on a rough horizontal surface. It starts off with a purely sliding motion at \(t =0\,s\). After \(2\,s\) it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after \(2\,s\) will be \(..............J\) (given, coefficient of friction is \(0.3\) and \(\left.g =10\,m / s ^2\right)\)

Which one of the following is the correct dimensional formula for the capacitance in F ? \(\mathrm{M}, \mathrm{L}, \mathrm{T}\) and C stand for unit of mass, length, time and charge,

As shown in the figure, a network of resistors is connected to a battery of \(2\,V\) with an internal resistance of \(3\,\Omega\). The currents through the resistors \(R_4\) and \(R_5\) are \(I_4\) and \(I_5\) respectively. The values of \(I_4\) and \(I_5\) are :

A \(20\, Henry\) inductor coil is connected to a \(10\, ohm\) resistance in series as shown in figure. The time at which rate of dissipation of energy (Joule’s heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor, is

A proton and an \(\alpha\)-particle are accelerated from rest by \(2\,V\) and \(4\,V\) potentials, respectively. The ratio of their de-Broglie wavelength is:

In an expression a \(\times 10^{\mathrm{b}}\) _______.

A spherical ball of radius \(1 \times 10^{-4} \mathrm{~m}\) and density \(10^5\) \(\mathrm{kg} / \mathrm{m}^3\) falls freely under gravity through a distance \(h\) before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of \(h\) is approximately _______. (The coefficient of viscosity of water is \(9.8 \times 10^{-6}\) \(\left.\mathrm{N} \mathrm{s} / \mathrm{m}^2\right)\)

Inside a uniform spherical shell \((a)\) the gravitational field is zero \((b)\) the gravitational potential is zero \((c)\) the gravitational field is same everywhere \((d)\) the gravitation potential is same everywhere \((e)\) all of the above Choose the most appropriate answer from the options given below