A simple pendulum of string length 30 cm performs 20 oscillations in 10s. The length of the string required for the pendulum to perform 40 oscillations in the same time duration is ___________ cm. [Assume that the mass of the pendulum remains same.]

An \(X-\)ray tube is operated at \(1.24\) million volt. The shortest wavelength of the produced photon will be ..... \(nm\)

The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure What is the value of current at \(t = 4\,s\) ? ............... \(\mu  A\)

Two guns \(A\) and \(B\) can fire bullets at speed \(1\, km/s\) and \(2\, km/s\) respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground 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\(^2\).)

Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to :-

What is the current through the battery in the circuit shown below?

Modern vacuum pumps can evacuate a vessel down to a pressure of \(4.0 \times {10^{ - 15}}\, atm\) at room temperature \((300\, K)\). Taking \(R = 8.0\, JK^{-1}\, mole^{-1}\) , \(1\, atm = 10^5\, Pa\) and \(N_ {Avogadro} = 6 \times 10^{23}\, mole^{-1}\) , the mean distance between molecules of gas in an evacuated vessel will be of the order of

Two coherent sources of light interfere. The intensity ratio of two sources is \(1: 4\). For this interference pattern if the value of \(\frac{I_{\max }+I_{\min }}{I_{\max _{\max }}-I_{\min }}\) is equal to \(\frac{2 \alpha+1}{\beta+3}\), then \(\frac{\alpha}{\beta}\) will be.

A particle executes simple harmonic motion and is located at \(x = a, b\)  and  \(c\) at times \(t_0, 2t_0\) and \(3t_0\) respectively. The frequency of the oscillation is