An emf of \(20\; \mathrm{V}\) is applied at time \(\mathrm{t}=0\) to a circuit containing in series \(10\; \mathrm{mH}\) inductor and \(5 \;\Omega\) resistor. The ratio of the currents at time \(\mathrm{t}=\infty\) and at \(t=40\; s\) is close to : (Take \(e^{2}=7.389\) )

A potential divider circuit is shown in figure. The output voltage \(V_0\) is _______.

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is

A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is \(\sqrt{\frac{2}{x}}\). The value of \(x\) is \(.......\)

The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have _________.

Two blocks of masses \(m\) and \(M,(M \gt m)\), are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released then
(\(\mu=\) coefficient of friction between the two blocks)

(A) The time period of small oscillation of the two blocks is \(\mathrm{T}=2 \pi \sqrt{\frac{(\mathrm{~m}+\mathrm{M})}{\mathrm{k}}}\)
(B) The acceleration of the blocks is \(\mathrm{a}=\frac{\mathrm{kx}}{\mathrm{M}+\mathrm{m}}\) (\(\mathrm{x}=\) displacement of the blocks from the mean position)
(C) The magnitude of the frictional force on the upper block is \(\frac{m \mu|x|}{M+m}\)
(D) The maximum amplitude of the upper block, if it does not slip, is \(\frac{\mu(M+m) g}{k}\)
(E) Maximum frictional force can be \(\mu(\mathrm{M}+\mathrm{m}) \mathrm{g}\).
Choose the correct answer from the options given below:

A block of mass 5 kg is moving on an inclined plane which makes an angle of \(30^{\circ}\) with the horizontal. Friction coefficient between the block and inclined plane surface is \(\frac{\sqrt{3}}{2}\). The force to be applied on the block so that the block will move down without acceleration is ___________ N.

An ideal gas goes from an initial state to final state. During the process, the pressure of gas increases linearly with temperature.
A. The work done by gas during the process is zero.
B. The heat added to gas is different from change in its internal energy.
C. The volume of the gas is increased.
D. The internal energy of the gas is increased.
E. The process is isochoric (constant volume process)
Choose the correct answer from the options given below:

A gas mixture consists of \(2\) moles of oxygen and 4 moles of neon at temperature \(T\). Neglecting all vibrational modes, the total internal energy of the system will be \(...........\,RT\)