Two iron solid discs of negligible thickness have radius \(R_1\) and \(R_2\) and moment of intertia \(I_1\) and \(I_2\), respectively. For \(R_2=2 R_1\), the ratio of \(I_1\) and \(I_2\) would be \(1 / x\), where \(\mathrm{x}=\) ________ -

A coil of negligible resistance is connected in series with \(90 \Omega\) resistor across \(120 \mathrm{~V}, 60 \mathrm{~Hz}\) supply. A voltmeter reads \(36 \mathrm{~V}\) across resistance. Inductance of the coil is _______.

A ball is spun with angular acceleration \(\alpha=6 t ^{2}-2 t\) where \(t\) is in second and \(\alpha\) is in \(rads\) \(^{-2}\). At \(t=0\), the ball has angular velocity of \(10\,rads\) \(^{-1}\) and angular position of \(4\,rad\). The most appropriate expression for the angular position of the ball is

A helicopter reises from rest on the ground vertically upwards with a constant acceleration \(g.\) A food packet is dropped from the helicopter when it is a height \(h\). The time taken by the packet to reach the ground is close to \([ g\) is the acceleration due to gravity]

The equilateral triangle \(ABC\) is cut from a thin solid sheet of wood. (See figure) \(D, E\) and \(F\) are the mid points of its sides as shown and \(G\) is the centre of the triangle. The moment of inertia of the triangle about an axis passing through \(G\) and perpendicular to the plane of the triangle is \(I_0.\) If the smaller triangle \(DEF\) is removed from \(ABC,\) the moment of inertia of the remaining figure about the same axis is \(I.\) Then

The charge accumulated on the capacitor connected in the following circuit is________ \(\mu \mathrm{C}\) (Given \(\mathrm{C}=150\  \mu \mathrm{F}\))

Consider a mixture of gas molecule of types \(A, B\) and \(C\) having masses \(m_{A}\,<\,m_{B}\,<\,m_{C}\) ratio of their root mean square speeds at normal temperature and pressure is :

The metallic bob of simple pendulum has the relative density \(5\). The time period of this pendulum is \(10\,s\). If the metallic bob is immersed in water, then the new time period becomes \(5 \sqrt{ x } s\). The value of \(x\) will be.

The mass defect in a particular reaction is \(0.4 \mathrm{~g}\). The amount of energy liberated is \(\mathrm{n} \times 10^7 \mathrm{kWh}\), where\(\mathrm{n}=\)________. (speed of light \(=3 \times 10^8 \mathrm{~m} / \mathrm{s}\) )

A ball is projected vertically upward with an initial velocity of \(50 \; ms ^{-1}\) at \(t =0 \; s\). At \(t =2 \,s\). another ball is projected vertically upward with same velocity. At \(t= \; \dots \; s\), second ball will meet the first ball \(\left( g =10 \; ms ^{-2}\right)\).