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The shown container contains liquid of variable density which varies as d = d0 (4 – 3y/h0) where h0 and d0 are constants and y is measured from the bottom of container. A small solid block density is The shown container contains liquid of variable density which varies as d = d0 (4 - 3y/h0) [...]

If velocity of a particle moving along a straight line changes sinusoidally with time as shown in the given graph. Find the average speed over time interval t = 0 to t = 2 (2n-1) seconds, n being any positive integer If velocity of a particle moving along a straight line changes sinusoidally with time [...]

A smooth piston of mass m, area of cross-section A is in equilibrium in a gas jar when pressure of the gas is P0. Find the angular frequency of oscillation of the piston, assuming adiabatic change of state of the gas. A smooth piston of mass m area of cross-section A is in equilibrium in [...]

In the shown arrangement, both the springs are in their natural lengths. The coefficient of friction between m2 and m1 is mu. There is no friction between m1 and the surface. If the blocks are displaced slightly, they together perform simple harmonic motion. both the springs are in their natural lengths. The coefficient of friction [...]

A vertical pole of length l, density rho, area of cross section A floats in two immiscible liquids of densities rho1 and rho2. In equilibrium position the bottom end is at the interface of the liquids. when the cylinder is displaced A vertical pole of length l area of cross section A floats in two [...]

In the arrangement as shown in the figure, the sleeve of mass M is fixed between two identical spring whose combined force constant is k. The sleeve can slide without friction over a horizontal bar AB. In the arrangement as shown in the figure the sleeve of mass M is fixed between two identical spring [...]

A body A of mass m1 = 1 kg and body B of mass m2 = 5.1 kg are interconnected by a spring as shown in figure. The body A performs free vertical harmonic oscillations with the amplitude 1.6 cm and frequency 25 Hz. attached to a spring of force constant k which is rigidly [...]

A rectangular tank having base 15 cm * 20 cm is filled with water (density rho = 1000 kg/m^3) up to 20 cm height. One end of an ideal spring of natural length h0 = 20 cm and force constant K = 280 N/m is fixed to the bottom of the tank so that the [...]

Figure shows a block P of mass m resting on a smooth horizontal surface, attached to a spring of force constant k which is rigidly fixed on the wall on left side, shown in the figure. At a distance l to the right of block there is a rigid wall. attached to a spring of [...]

Figure (a) shows a spring block system, hanging in equilibrium. The block of system is pulled down by a distance x and imparted a velocity v in downward direction as shown in Fig. (b). Find the time it will take to reach its mean position. Figure (a) shows a spring block system hanging in equilibrium. [...]