Physics Test 158

A simple pendulum swings with angular amplitude θ_o in vertical plane. The tension in the swing when it is vertically lowest position is twice the tension in it’s extreme position then cos θ_o is equal to

A tank accelerates upward with acceleration a = 1 m/sec² contains water. A block of mass 1 kg and density 0.8 gm/cm³ is held stationary inside the tank with help of the string as shown in figure. The tension in string is

For the situation shown in figure, water flows on the surface of a fixed plate. The velocity of water a function of distance ‘y’ is given as . Determine the magnitude of shear stress that the water applies at the base of plate. Coefficient of viscosity is η

In the ideal atwood machine arrangement shown in figure, the change in kinetic energy (in Joules) of system during 3^rd second of their motion starting from rest is

Two steel wires of same length but radii r and 2r respectively connected together end to end and tide to a wall as shown in figure. The force stretches the combination by 10mm. The displacement of mid point A is:

Two boys each of mass 50 kg are at the ends of uniform 4m long platform of mass 95 kg moving 2 m/sec on a smooth surface. The boy at the rear end has a ball of mass 5 kg also which he rolls towards the front end at 4m/sec relative to himself. How far has the platform moved by the time the ball is caught by boy at other end ?

3 identical blocks shown in figure. If A and C are moving together at 12m/sec and B is at rest when A hits B as shown, collision is perfectly inelastic. The friction coefficient between A and C is same as that between B and C and is equal to 0.2. Finally C is on top of B and all blocks are moving together with same speed. What is the length of each block if ground is perfectly smooth ?

The angular velocity of a body moving in circular path is shown in graph below. What is the average angular velocity for the entire motion?

A block of mass 2 kg is sitting on a vertical spring and compressing it by 4 cm. Another block of mass 1 kg in dropped on it from a height of 45 cm. The block stick together after collision. What is the maximum compression of the spring?

Two beads of mass m and 2 m are connected by massless rod of length R and threaded on to a smooth circular wire of radius R. When the wire rotates uniformly about a vertical diameter, the beads do not slide on it and rod remains vertical as shown. What must be the angular velocity ω of the wire, if radius a circular wire  ?