\(100\) balls each of mass moving with speed \(v\) simultaneously strike a wall normally and reflected back with same speed, in time \(t s\). The total force exerted by the balls on the wall is

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\(^2\).)

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is \(11.2 \mathrm{~km} / \mathrm{s}\), the escape velocity in \(\mathrm{km} / \mathrm{s}\) from the planet will be :

The stored charge in the capacitor in steady state of the following circuit is ________ \(\mu\)C.

An engine approaches a hill with a constant speed. When it is at a distance of \(0.9\, km\), it blows a whistle whose echo is heard by the driver after \(5\, seconds\). If the speed of sound in air is \(330\, m/s\), then the speed of the engine is .... \(m/s\)

The ratio of momentum of the photons of the \(1^{st}\) and \(2^{nd}\) line of Balmer series of Hydrogen atoms is \(\alpha/\beta\). The possible values of \(\alpha\) and \(\beta\) are:-

The radius of electron's second stationary orbit in Bohr's atom is \(R\). The radius of \(3 rd\) orbit will be \(.........R\)

A car \(P\) travelling at \(20\,ms ^{-1}\) sounds its horn at a frequency of \(400\,Hz\). Another car \(Q\) is travelling behind the first car in the same direction with a velocity \(40\,ms ^{-1}\). The frequency heard by the passenger of the car \(Q\) is approximately \(.......\,Hz\) [Take, velocity of sound \(=360\,ms ^{-1}\) ]

Two identical conducting spheres \(A\)  and \(B,\)  carry equal charge. They are separated by a distance much larger than their diameter, and the force between them is \(F\) . A third identical conducting sphere, \(C,\)  is uncharged. Sphere \(C\)  is first touched to \(A,\) then to \(B,\)  and then removed. As a result, the force between \(A\)  and \(B\)  would be equal to

Two parallel plate capacitors of capacity \(C\) and \(3\,C\) are connected in parallel combination and charged to a potential difference \(18\,V\). The battery is then disconnected and the space between the plates of the capacitor of capacity \(C\) is completely filled with a material of dielectric constant \(9\). The final potential difference across the combination of capacitors will be \(V\)

Two point charges of 1 nC and 2 nC are placed at the two corners of equilateral triangle of side 3 cm. The work done in bringing a charge of 3 nC from infinity to the third corner of the triangle is ________ \(\mu\)J.
(\(\frac{1}{4\pi\epsilon_{0}} = 9 \times 10^{9}\ N.m^{2}/C^{2}\))

A plano-convex lens having radius of curvature of first surface 2 cm exhibits focal length of \(f_1\) in air. Another plano-convex lens with first surface radius of curvature 3 cm has focal length of \(\mathrm{f}_2\) when it is immersed in a liquid of refractive index 1.2 . If both the lenses are made of same glass of refractive index 1.5 , the ratio of \(f_1\) and \(f_2\) will be _______.