A stone is dropped from the top of a tall cliff and n seconds later another stone is thrown vertically downwards with velocity u. Then the second stone overtakes the first, below the top of cliff at a distance given by
A small hollow sphere, which has a small hole in it, is immersed in water to a depth of 0.5 m before any drop penetrates into it. If surface tension for water is 0.073 N/m, the radius of the hole is
A neutron is moving with velocity u. It collides head on and elastically with an atom of mass number A. If the initial kinetic energy of the neutron is E, how much kinetic energy is retained by neutron after collision?
A toy gun uses a spring of force constant k. When charged before being triggered in the upward direction the spring is compressed by x. If the mass of the shot is m, on being triggered, it will go up to a height of
A tuning fork P has a frequency 3% more than that of a standard fork. A second fork Q has a frequency 2% less than that of the standard fork. When P and Q are sounded together the number of beats produced per second is 8. The frequency of fork Q is
Two blocks A and B, each of mass m are connected by a massless spring of natural length L and spring constant k. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length as shown. A third identical block C, also of mass m, moves on the floor with a speed v along the line joining A and B and collides with A. Then the
A)
Kinetic energy of the A - B system, at maximum compression of the spring, is zero
doneclear
B)
Kinetic energy of the A - B system, at maximum compression of the spring, is \[m{{v}^{2}}/4\]
doneclear
C)
Maximum compression of the spring is \[v\sqrt{mk}\]
doneclear
D)
Maximum compression of the spring is \[v\sqrt{m/k}\]
A triangular block ABC of mass m and sides 2a lies on a smooth horizontal plane as shown in figure. Three point masses of mass m each strike the block at A, B and C with speeds v as shown. After the collision the particles come to rest. Then the angular velocity acquired by the triangular block is (l is the moment of inertia of the triangular block about G perpendicular to the plane of the block)
Two blocks with masses \[{{m}_{1}}=1kg\] and \[{{m}_{2}}=2kg\] are connected by a spring of spring constant k= 24 N/m and placed on a frictionless horizontal surface as shown in figure. The block \[{{m}_{1}}\] is imparted an initial velocity \[{{\text{v}}_{0}}=12\text{ }cm/s\] to the right. The amplitude of oscillation is