A voltage regulating circuit consisting of Zener diode, having break-down voltage of 10 V and maximum power dissipation of 0.4 W , is operated at 15 V . The approximate value of protective resistance in this circuit is _________ \(\Omega\).

A disc is rolling without slipping on a surface. The radius of the disc is \(R\). At \(t=0\), the top most point on the disc is \(A\) as shown in figure. When the disc completes half of its rotation, the displacement of point \(A\) from its initial position is

If the time period of a two meter long simple pendulum is \(2\, s\), the acceleration due to gravity at the place where pendulum is executing \(S.H.M.\) is

A mass \(M\) hangs on a massless rod of length \(l\) which rotates at a constant angular frequency. The mass \(M\) moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity \(\omega .\) The angular momentum of \(M\) about point \(A\) is \(L _{ A }\) which lies in the positive \(z\) direction and the angular momentum of \(M\) about \(B\) is \(L _{ B }\). The correct statement for this system is

A ball of mass \(160\, g\) is thrown up at an angle of \(60^o\) to the horizontal at a speed of \(10\, m\,s^{-1}\) . The angular momentum of the ball at the highest point of the trajectcry with respect to the point from which the ball is thrown is nearly ........ \(kg\, m^2/s\)  \((g\, = 10\, m\,s^{-2})\)

The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit) :

In a microscope the objective is having focal length \(f_0=2 cm\) and eye-piece is having focal length \(f_{ e }=4 cm\). The tube length is 32 cm . The magnification produced by this microscope for normal adjustment is _________ .

Two point charges \(8 \, \mu C\) and \(-2 \, \mu C\) are located at \(x = 2\) cm and \(x = 4\) cm, respectively on the \(x\)-axis. The ratio of electric flux due to these charges through two spheres of radii \(3\) cm and \(5\) cm with their centers at the origin is _______.

A potential divider circuit is connected with a DC source of \(20 \mathrm{~V}\), a light emitting diode of glow in voltage \(1.8 \mathrm{~V}\) and a zener diode of breakdown voltage of \(3.2 \mathrm{~V}\). The length (PR) of the resistive wire is \(20 \mathrm{~cm}\). The minimum length of \(P Q\) to just glow the LED is _______ cm.

A body moves on a frictionless plane starting from rest. If \(\mathrm{S}_{\mathrm{n}}\) is distance moved between \(\mathrm{t}=\mathrm{n}-1\) and \(\mathrm{t}\) \(=\mathrm{n}\) and \(\mathrm{S}_{\mathrm{n}-1}\) is distance moved between \(\mathrm{t}=\mathrm{n}-2\) and \(t=n-1\), then the ratio \(\frac{S_{n-1}}{S_n}\) is \(\left(1-\frac{2}{x}\right)\) for \(n\) \(=10\). The value of \(x\) is _______.