A body rotating with an angular speed of \(600\, {rpm}\) is uniformly accelerated to \(1800 \,{rpm}\) in \(10\; sec\). The number of rotations made in the process is ..... .

A circular disc \(D_1\) of mass \(M\) and radius \(R\) has two identical discs \(D_2\) and \(D_3\) of the same mass \(M\) and radius \(R\) attached rigidly as its opposite ends (see figure). The moment of inertia of the system about the axis \(OO\)’, passing through the centre of \(D_1\) as shown in the figure, will

In an experiment to measure focal length \((f)\) of convex lens, the least counts of the measuring scales for the position of object \((u)\) and for the position of image \((v)\) are \(\Delta u\) and \(\Delta v\), respectively. The error in the measurement of the focal length of the convex lens will be _______.

A uniform solid cylinder of length \(L\) and radius \(R\) has moment of inertia about its axis equal to \(I_1\). A small co-centric cylinder of length \(L / 2\) and radius \(R / 3\) carved from this cylinder has moment of inertia about its axis equals to \(I_2\). The ratio \(I_1 / I_2\) is _________ .

Identify the correct truth table of the given logical circuit.

The root mean square speed of molecules of a given mass of a gas at \(27^{\circ} C\) and \(1\) atmosphere pressure is \(200\, ms ^{-1}\). The root mean square speed of molecules of the gas at \(127^{\circ} C\) and \(2\) atmosphere pressure is \(\frac{ x }{\sqrt{3}}\, ms ^{-1} .\) The value of \(x\) will be ......\(ms ^{-1} .\)

An object is allowed to fall from a height \(R\) above the earth, where \(R\) is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be :

A body \(A\) of mass \(\mathrm{m}\) is moving in a circular orbit of radius \(\mathrm{R}\) about a planet. Another body \(\mathrm{B}\) of mass \(\frac{\mathrm{m}}{2}\) collides with \(\mathrm{A}\) with a velocity which is half \(\left(\frac{\overrightarrow{\mathrm{v}}}{2}\right)\) the instantaneous velocity \(\overrightarrow{\mathrm{v}}\) of \(\mathrm{A}\) The collision is completely inelastic. Then, the combined body

The mass per unit length of a uniform wire is \(0.135\, g / cm\). A transverse wave of the form \(y =-0.21 \sin ( x +30 t )\) is produced in it, where \(x\) is in meter and \(t\) is in second. Then, the expected value of tension in the wire is \(x \times 10^{-2} N\). Value of \(x\) is . (Round-off to the nearest integer)