A body of mass \( m \) and radius \( r \) rolling horizontally with velocity \( V \), rolls up an inclined plane to a vertical height \( \frac{V^2}{g} \). The body is:
A capacitor of capacitance ‘C’ is charged to a potential ‘V’ and disconnected from the battery. Now if the space between the plates is completely filled with a substance of dielectric constant ‘K’, the final charge and the final potential on the capacitor are respectively:
For a gas in a thermodynamic process, the relation between internal energy (U), the pressure (P), and the volume (V) is given by: \[ U = 3 + 1.5PV \] The ratio of the specific heat capacities of the gas at constant volume and constant pressure is:
At a pressure \( P \) and temperature \( 127^\circ C \), a vessel contains 21 g of a gas. A small hole is made into the vessel so that the gas leaks out. At a pressure of \( \frac{2P}{3} \) and a temperature of \( t^\circ C \), the mass of the gas leaked out is 5 g. Then \( t \) is:
When the object and the screen are 90 cm apart, it is observed that a clear image is formed on the screen when a convex lens is placed at two positions separated by 30 cm between the object and the screen. The focal length of the lens is:
The following orbital energies (\(E\)) are compared. Identify the correct sets
(I) E2(H) = E2(H)(II) E3(H) = E3(He)(III) E2s(H) < E2s(He)(IV) E3s(He) < E3s(H)
Consider a circuit where a cell of emf \( E_0 \) and internal resistance \( r \) is connected across the terminal A and B as shown in the figure. The value of \( R \) for which the power generated in the circuit is maximum, is given by: