If Surface tension \((S)\), Moment of Inertia \((I)\) and Planck’s constant \((h)\), were to be taken as the fundamental units, the dimensional formula for linear momentum would be

A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity)

\({ }_{92}^{238} A \rightarrow{ }_{90}^{234} B +{ }_2^4 D + Q\) In the given nuclear reaction, the approximate amount of energy released will be \(.....\,MeV\) \(\text { [Given, mass of }{ }_{92}^{238} A =238.05079 \times 931.5\,MeV / c ^2\) \(\text { mass of }{ }_{90}^{234} B =234.04363 \times 931.5\,MeV / c ^2\) \(\text { mass of } \left.{ }_2^4 D =4.00260 \times 931.5\,MeV / c ^2\right]\)

Eight copper wire of length \(l\) and diameter \(d\) are joined in parallel to form a single composite conductor of resistance \(R\). If a single copper wire of length \(2\,l\) have the same resistance \((R)\) then its diameter will be \(.....d\).

The heat absorbed by a system in going through the given cyclic process is _______.

The pressure acting on a submarine is \(3 \times 10^{5}\;Pa\) at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be: (Assume that atmospheric pressure is \(1 \times 10^{5} \;Pa\) density of water is \(10^{3}\, kg \,m ^{-3}, g =10 \,ms ^{-2}\) )

Given below are two statements: One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\): If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude. Reason \(R \): At equator, the direction of acceleration due to the gravity is towards the center of earth. In the light of above statements, choose the correct answer from the options given below

In interference experiment the path difference between two interfering waves at a point \(A\) on the screen is \(\lambda/3\), where \(\lambda\) is the wavelength of these waves, and at another point \(B\) the path difference is \(\lambda/6\). The ratio of intensities at points \(A\) and \(B\) is _______.

In a circuit for finding the resistance of a galvanometer by half deflection method, a  \(6\,V\)  battery and a high resistance of  \(11\,k\Omega \)  are used. The figure of merit of the galvanometer \(60\,\mu A/\)  division. In the absence of shunt resistance, the galvanometer produces a deflection of  \(\theta = 9\)  divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of \(\theta /2 ,\)  is closest to ..................  \(\Omega\)