A body of mass \(2\) \(kg\) revolves in a circle of diameter \(40cm\), making \(120\) \(rpm\). What will be the (i) linear velocity and (ii) centripetal acceleration of the body?
Ans:(i) \(0.8\pi m.s^{-1}\) and (ii) \(3.2\pi^{2} m.s^{2}\).
The angular velocity of a particle moving along a circle of radius \(50cm\) is increased in \(5\) minutes from \(100\) \(rpm\) to \(400\) \(rpm\). Then calculate: (i) Angular Acceleration and (ii) Linear Acceleration.
Ans:(i) \(\frac{\pi}{30}rad.s^{-2}\) and (ii) \(\frac{5\pi}{3}cm.s^{-2}\).
Calculate: the magnitude of total linear acceleration of a particle moving in a circular path of radius \(0.5m\), at the instant, when its angular velocity is \(2.5\) \(rad.s^{-1}\) and its angular acceleration is \(6\) \(rad.s^{-2}\).
Ans: \(4.33m.s^{-2}\).
A particle of mass \(42g\) attached to a string of \(60cm\) in length is whirled in a horizontal circle. If, period of revolution is \(2s\). Then find the tension in the string?
Ans: \(Tension=24846 dyn\).
A string breaks under a load of \(5kg\). A mass of \(1kg\) is attached to one end of the string \(10m\) long and rotates in a horizontal circle. Calculate: the greatest number of revolutions that the mass can make without breaking the string?
Ans: \(\left(1.114\right) r.p.m.\)
A car moving with a speed of \(54kmh^{-1}\) negotiates a level circular road of radius \(10m\). What should be the co-efficient of friction so that car may not skid-off the road?
Ans: \(\mu=2.29\)
What should be the angle through which a cyclist bends from the vertical when he crosses a circular path of radius \(r\) and circumference of \(34.3m\) in \(\sqrt{22}s\). Take: \(g=9.8 ms^{-2}\).
Ans: \(\theta=45^{o}\).
A cyclist speeding \(6ms^{-1}\) in a circular path of radius \(18m\) makes an angle \(\theta\) with the vertical. Calculate: The magnitude of the \(\theta\). Also, co-efficient of friction between the tires and the ground?
Ans: \(11^{o}\) and \(0.2041\).
A car of mass \(2000kg\) is moving with a speed \(15ms^{-1}\) on a circular path of radius \(20m\) on a levelled road. What should be the frictional force between car and the road so that car may not slip? Also, find the value of co-efficient of frictional force?
Ans: \(\left(2.25\times 10^{4}\right)N\) and \(\mu=1.147\).
A train has to negotiate a curve of \(400m\) in radius. By how much the outer edge of the rail be raised with respect to the inner rail for a speed of \(54kmh^{-1}\)? Given: Distance between rail is \(1m\) and friction between track and wheels is very very small.
