A block of mass \(m\), is placed on a smooth sphere of radius \(R\) and slides down when pushed slightly. At what distance \(h\) vertically downward from the top pf the sphere, will it leave the sphere?
Ans: \(H=\frac{R}{3}\)
A tube of length \(L\) is fitted completely with an incompressible liquid of mass \(M\) and closed at the both ends. The tube is rotated in a horizontal plane about one of its ends with uniform angular speed \(\omega\). The force exerted by the liquid at the other end will be?
Ans: \(\frac{1}{2}M\omega^{2}L\).
With what maximum acceleration can a fireman slides down a rope whose breaking strength is two-third of the weight of the fireman? Given: The maximum force that fireman can apply on the rope is half of its weight and co-efficient of friction is \(\mu\).
Ans: \(\frac{g}{3}\)
A bob of mass \(200g\) is suspended by a string of \(20cm\) length. Keeping the string always taut, the ball describes a horizontal circle of radius \(10cm\). Calculate: The periodic time of this conical pendulum and the tension in the string?
Ans: \(\omega=5.31rad.s^{-1}\).
A sphere of mass \(400g\) is attached to an inextensible string of length \(130cm\) whose upper end is fixed to a celling. The sphere is made to describe a horizontal circle of radius \(50cm\). Calculate: the (i) periodic time of this conical pendulum and (ii) tension in the string?
Ans:(i) \(2.19s\) and (ii) \(4.24N\)
A particle describes describes a horizontal circle on a smooth horizontal surface of an inverted cone. The height of the plane of the circle above the vertex of the inverted cone is \(10cm\). Find: the speed of the particle. Take: \(g=9.8ms^{-2}\).
Ans: \(v=1m.s^{-1}\).
A tube of length \(L\) is fitted completely with an incompressible liquid of mass \(M\) and closed at both ends. The tube is rotated in a vertical plane about one of its ends, with an uniform angular speed \(\omega\). Then, calculate the force exerted by liquid in the tube when angular displacement with respect to horizontal direction is, (i) \(0^{o}\) (ii) \(90^{o}\) (iii) \(180^{o}\) and (iv) \(270^{o}\).
