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 cells, when connected either in parallel or in series gives same current in an external resistance $5 \Omega$ The internal resistance of each cell will be__ $\Omega$
A thin rod having a length of \(1 m\) and area of cross-section \(3 \times 10^{-6} m ^2\) is suspended vertically from one end. The rod is cooled from \(210^{\circ} C\) to \(160^{\circ} C\) After cooling, a mass \(M\) is attached at the lower end of the rod such that the length of rod again becomes \(1m\). Young's modulus and coefficient of linear expansion of the rod are \(2 \times 10^{11} N m ^{-2}\) and \(2 \times 10^{-5} K ^{-1}\), respectively. The value of \(M\) is ____ \(kg\). (Take \(g =10 \ m s ^{-2}\))
A solid sphere of mass $1 \,kg$ rolls without slipping on a plane surface Its kinetic energy is $7 \times 10^{-3} J$. The speed of the centre of mass of the sphere is ___$cm s ^{-1}$.
For hydrogen atom, $\lambda_1$ and $\lambda_2$ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure The ratio of $\lambda_1$ and $\lambda_2$ is $\frac{x}{32}$ The value of $x$ is
100 balls each of mass $m$ 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 drift velocity of electrons for a conductor connected in an electrical circuit is $V _{ d }$ The conductor in now replaced by another conductor with same material and same length but double the area of cross section The applied voltage remains same The new drift velocity of electrons will be
The correct relation between $\gamma=\frac{ c _{ p }}{ c _{ v }}$ and temperature $T$ is :
The pressure of a gas changes linearly with volume from $A$ to $B$ as shown in figure If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be Is
If $R , X _{ L }$, and $X _{ C }$ represent resistance, inductive reactance and capacitive reactance Then which of the following is dimensionless :
Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height Choose the correct statement out of the following (Assume negligible air friction)