A sphere of mass \(10Kg\) rolls on a flat surface without slipping with a speed of \(50\frac{cm}{sec}\). Calculate: total energy in Joule.
Ans: \(K=1.75J\).
An angular disc of mass \(100g\) and radii \(20cm\) & \(25cm\) rolls such that its center has a velocity of \(50\frac{cm}{s}\). What will be the K.E of the disc if M.I of angular disc = \(\frac{1}{2} m \left(R_{1}^{2}+R_{2}^{2}\right)\)?
Ans: \(K.E=\left(2.3\times10^{5}\right)erg\).
A cylinder of mass \(5Kg\) and radius \(30cm\) is rolling down an inclined plane at an angle of \(45^{o}\) with the horizontal. Calculate: (i) Force of friction? (ii) Acceleration with which the cylinder rolls down? and (iii) The minimum value of static friction so that the cylinder does not slip while rolling down the plane.
Ans:(i) \(f_{firction}=11.55N\) (ii) \(a=4.62\frac{m}{s^{2}}\) and (iii) \(\mu_{static}=frac{1}{3}\).
Two identical spheres, one hollow and other solid are made to roll down an inclined plane making an angle \(\Theta\) with the horizontal. Which one of them reaches the bottom of the inclined plane earlier?
Ans: \(a_{1}>a_{2}\).
A body of mass \(5Kg\) is attached to a weightless string wound around a cylinder of mass \(8kg\) and radius \(0.3m\). The body is allowed to fall. Calculate: (i) Tension in the string? Ans: \(T=21.78N\) (ii) Acceleration with which body falls? Ans: \(a=5.44\frac{m}{s^{2}}\) (iii) Angular Acceleration, \(\alpha\)? Ans: \(\alpha=18.13\frac{rad}{s^{2}}\)
A particle of mass ‘m’ is moving in a circular orbit of radius ‘r’ has angular momentum ‘L’ about its center. Calculate: The kinetic energy of the particle in terms of L, m and r?
Ans: \(K.E=\frac{L^{2}}{2mr^{2}}\).
If the angular momentum of a rotating body about a fixed axis is increased by \(10\%\). Find the percentage increase in rotational kinetic energy.
