Physics Test 10...

Two blocks A and B of masses m and 2m respectively are connected by a spring of force constant k. The masses are moving to the right with uniform velocity v = 10m/s each, the heavier mass leading the lighter one. The spring in between them is of natural length during the motion. Block B collides with a third block C of mass m, at rest. The collision being completely inelastic. Find minimum speed (in m/s) of block A in the subsequent motion.

In the given circuit diagram, switch was connected to position 1 for long time. At t = 0, switch is shifted from position 1 to position 2. Find the final charge on capacitor 2C. 

The region between two concentric spheres of radii R₁ and R₂(R₁ < R₂) has volume charge density ρ = b/r , where b is constant and r is the radial distance. A point charge q = 16 µC is placed at the origin, r = 0. Find the value of b (in SI units) for which the electric field in the region between spheres is constant.  (Take : R₂ = 2R₁ = 4/√π  mm ).

A hollow hemi-sphere of mass m and radius r is released from rest in the position shown. Knowing that the hemi-sphere rolls without sliding. Determine the reaction at the horizontal surface at the instant when  it has rolled through 90°.

Observer standing at the sea coast observes 30 waves reaching the coast per minute. The wavelength of each wave is 10m. When observer drives a boat in sea against waves, with velocity 5 m/sec then n waves strikes the boat per minute. Velocity of wave and value of n is respectively (in SI units)

In a meter Bridge experiment the resistance of resistance box is 16 Ω , which is inserted in right gap. The null point is obtained at 25cm from the left end. The leastcount for meter scale is 1mm. The percentage error in calculating unknown resistance is approximately:

A source contains two phosphorus radionuclides  How long one must wait until 90% to do so?

Two blocks A and B of same mass M are connected with each other with an ideal string of length 2ℓ passing over an ideal pulley. The block A is connected to a light pan C with an ideal string as shown in figure. A particle of mass M/2 is dropped on pan from height ℓ / 2 as shown. If collision between particle and pan is perfectly inelastic, acceleration of B just after the collision, is :-

Figure shows a large closed cylindrical tank containing water. Initially, the air trapped above the water surface has a height h₀ and pressure 2P₀ where P₀ is the atmospheric pressure. There is a hole in the wall of the tank at a depth h₁ below the top from which water comes out. A long vertical tube is connected as shown. Find the distance of water surface  in the long tube from the top of the tank, when the water stops coming out of the hole.