The charge stored by the capacitor C in the given circuit in the steady state is _________ \(\mu C\).

A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J , then the mass of the bullet is __________ grams.
(Latent heat of fusion of lead \(=2.5 \times 10^4 \mathrm{JKg}^{-1}\) and specific heat capacity of lead \(=125 \mathrm{JKg}^{-1}\) \(\left.\mathrm{K}^{-1}\right)\)

The increase in the pressure required to decrease the volume \((\Delta V)\) of water is \(6.3 \times 10^7\) N/m\(^2\). The percentage decrease in the volume is _____. (Bulk modulus of water \(= 2.1 \times 10^9\) N/m\(^2\).)

The speed of a swimmer is \(4\,km\,h ^{-1}\) in still water. If the swimmer makes his strokes normal to the flow of river of width \(1\,km\), he reaches a point \(750 \,m\) down the stream on the opposite bank.The speed of the river water is \(.........km h ^{-1}\)

Two identical metallic spheres \(A\) and \(B\) when placed at certain distance in air repel each other with a force of \(F\). Another identical uncharged sphere \(C\) is first placed in contact with \(A\) and then in contact with \(B\) and finally placed at midpoint between spheres \(A\) and \(B\). The force experienced by sphere \(C\) will be.

One end of a straight uniform \(1\; \mathrm{m}\) long bar is pivoted on horizontal table. It is released from rest when it makes an angle \(30^{\circ}\) from the horizontal (see figure). Its angular speed when it hits the table is given as \(\sqrt{\mathrm{n}}\; \mathrm{s}^{-1},\) where \(\mathrm{n}\) is an integer. The value of \(n\) is

A sliver wire has mass \((0.6 \pm 0.006) \; g\), radius \((0.5 \pm 0.005) \; mm\) and length \((4 \pm 0.04) \; cm\). The maximum percentage error in the measurement of its density will be \(......\,\%\)

In an experiment with sonometer when a mass of \(180\,g\) is attached to the string, it vibrates with fundamental frequency of \(30\,Hz\). When a mass \(m\) is attached, the string vibrates with fundamental frequency of \(50\,Hz\). The value of \(m\) is \(.........\,g\).