A homogeneous solid cylindrical roller of radius \(R\) and mass \(M\) is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is

A heat engine is involved with exchange of heat of \(1915\, J,\) \(-40\, J ,+125\, J\) and \(-Q\,J\), during one cycle achieving an efficiency of \(50.0 \%\). The value of \(Q\) is.......\(J\)

A thin \(1 \,m\) long rod has a radius of \(5\, mm\). A force of \(50\,\pi kN\) is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is \(0.01\, mm\), which of the following statements is false ?

An object with mass 500 g moves along x -axis with speed \(v=4 \sqrt{x} \mathrm{~m} / \mathrm{s}\). The force acting on the object is :

The initial velocity \(v_{i}\) required to project a body vertically upward from the surface of the earth to reach a height of \(10\, R ,\) where \(R\) is the radius of the earth, may be described in terms of escape velocity \(v_{ e }\) such that \(v_{i}=\sqrt{\frac{x}{y}} \times v_{ e } .\) The value of \(x\) will be ...... .

In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are \(70 \mathrm{~ms}^{-1}\) and \(65 \mathrm{~ms}^{-1}\) respectively. If the wing area is \(2 \mathrm{~m}^2\) the lift of the wing is _______ \(\mathrm{N}\). (Given density of air \(=1.2 \mathrm{~kg} \mathrm{~m}^{-3}\) )

Which one is the correct option for the two different thermodynamic processes ?

A boy’s catapult is made of rubber cord which is \(42\, cm\) long, with \(6\, mm\) diameter of cross -section and of negligible mass. The boy keeps a stone weighing \(0.02\, kg\) on it and stretches the cord by \(20\, cm\) by applying a constant force. When released, the stone flies off with a velocity of \(20\, ms^{-1}\). Neglect the change in the area of cross section of the cord while stretched. The Young’s modulus of rubber is closest to