A bob of heavy mass m is suspended by a light string of length l. The bob is given a horizontal velocity $v_{0}$ as shown in figure. If the string gets slack at some point P making an angle $\theta$ from the horizontal, the ratio of the speed v of the bob at point P … Read more
In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency $\omega(t)$ and average amplitude $A(t)$ of the system change with time t. Which one of the following options schematically depicts these changes … Read more
A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is:
The output (Y) of the given logic implementation is similar to the output of an/a ____ gate.
A balloon is made of a material of surface tension S and its inflation outlet (from where gas is filled in it) has small area A. It is filled with a gas of density $\rho$ and takes a spherical shape of radius R. When the gas is allowed to flow freely out of it, its … Read more
A full wave rectifier circuit with diodes ($D_1$) and ($D_2$) is shown in the figure. If input supply voltage $V_{in} = 220\sin(100\pi t)$ volt, then at $t = 15$ msec
The electric field in a plane electromagnetic wave is given by $E_{z}=60~\cos(5x+1.5\times10^{9}t)V/m.$ Then expression for the corresponding magnetic field is (here subscripts denote the direction of the field):
Consider the diameter of a spherical object being measured with the help of a Vernier callipers. Suppose its 10 Vernier Scale Divisions (V.S.D.) are equal to its 9 Main Scale Divisions (M.S.D.). The least division in the M.S. is 0.1 cm and the zero of V.S. is at $x=0.1$ cm when the jaws of Vernier … Read more
Two gases A and B are filled at the same pressure in separate cylinders with movable pistons of radius $r_{A}$ and $r_{B}$, respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure, the pistons of gas A and B are displaced by 16 cm and 9 cm, respectively. If … Read more
A ball of mass 0.5 kg is dropped from a height of 40 m. The ball hits the ground and rises to a height of 10 m. The impulse imparted to the ball during its collision with the ground is (Take $g=9.8~m/s^{2})$