A uniform disc with mass \(M=4\,kg\) and radius \(R=\) \(10\,cm\) is mounted on a fixed horizontal axle as shown in figure. A block with mass \(m =2\,kg\) hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is_______ \(N\) \(\left(\right.\) Take \(\left.g =10\,ms ^{-2}\right)\)

The dimensional formula of latent heat is _______.

A \(110 \; V , 50 \; Hz , AC\) source is connected in the circuit (as shown in figure). The current through the resistance \(55 \; \Omega\), at resonance in the circuit, will be \(\dots \; A\).

An infinite plane sheet of charge having uniform surface charge density \(+\sigma_5 \mathrm{C} / \mathrm{m}^2\) is placed on \(\mathrm{x}-\mathrm{y}\) plane. Another infinitely long line charge having uniform linear charge density \(+\lambda_e \mathrm{C} / \mathrm{m}\) is placed at \(z=4 \mathrm{~m}\) plane and parallel to \(y\)-axis. If the magnitude values \(\left|\sigma_s\right|=2\left|\lambda_{\mathrm{e}}\right|\) then at point \((0,0,2)\), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is \(\pi \sqrt{\mathrm{n}}: 1\). The value of \(n\) is _______.

Given below are two statements: one is labelled as Assertion \(\mathbf{A}\) and the other is labelled as Reason \(\mathbf{R}\)
Assertion A: In a central force field, the work done is independent of the path chosen.
Reason R: Every force encountered in mechanics does not have an associated potential energy.
In the light of the above statements, choose the most appropriate answer from the options given below

The de Broglie wavelengths of a proton and an \(\alpha\) particle are \(\lambda\) and \(2 \lambda\) respectively. The ratio of the velocities of proton and \(\alpha\) particle will be _______.

A thin rod of mass \(0.9\, kg\) and length \(1 \,m\) is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move \(0.1\, kg\) moving in a straight line with velocity \(80\,m / s\) hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in \(rad/s\)) of the rod immediately after the collision will be

Four capacitor each of capacitance \(16 \mu \mathrm{~F}\) are connected as shown in the figure. The capacitance between points A and B is : ______ (in \(\mu \mathrm{F}\)).

A concave mirror for face viewing has focal length of \(0.4\,m.\) The distance at which you hold the mirror from your face in order to see your image upright with a magnification of \(5\) is......\(m\)