One main scale division of a vernier callipers is \(a\) \(cm\) and \(n ^{\text {th }}\) division of the vernier scale coincide with \(( n -1)^{\text {th }}\) division of the main scale. The least count of the callipers in \(mm\) is

A rigid wire consists of a semicircular portion of radius \(R\) and two straight sections. The wire is partially immerged in a perpendicular magnetic field \(B=B_0\ {j}\) as shown in figure. The magnetic force on the wire if it has a current \(i\) is _______.

At \(t=0\), a body of mass \(100\) g starts moving under the influence of a force \((5\hat{i}+10\hat{j})\) N. After \(2\) s its position is \((2x\hat{i}+5y\hat{j})\) m. The ratio \(x:y\) is ______.

A uniform sphere of weight \(W\) and radius \(5\, cm\) is being held by a string as shown in the figure. The tension in the string will be

If \(B\) is magnetic field and \(\mu_0\) is permeability of free space, then the dimensions of \(\left(B / \mu_0\right)\) is

Two cells of emf 1 V and 2 V and internal resistance \(2 \Omega\) and \(1 \Omega\), respectively, are connected in series with an external resistance of \(6 \Omega\). The total current in the circuit is \(\mathrm{I}_1\). Now the same two cells in parallel configuration are connected to same external resistance. In this case, the total current drawn is \(I_2\). The value of \(\left(\frac{I_1}{I_2}\right)\) is \(\frac{x}{3}\). The value of \(x\) is _____.

At room temperature a diatomic gas is found to have an \(r.m.s.\) speed of \(1930\,ms^{-1}\). The gas is

The energy of an electromagnetic wave contained in a small volume oscillates with

Match List \(I\) with List \(II\)

LIST \(I\)	LIST \(II\)
\(A\) Planck's constant \(( h )\)	\(I\) \(\left[ M ^1 L ^2 T ^{-2}\right]\)
\(B\) Stopping potential \(( Vs )\)	\(II\) \(\left[ M ^1 L ^1 T ^{-1}\right]\)
\(C\) Work function \((\phi)\)	\(III\) \(\left[ M ^1 L ^2 T ^{-1}\right]\)
\(D\) Momentum \(( p )\)	\(IV\) \(\left[ M ^1 L ^2 T ^{-3} A ^{-1}\right]\)

Match List - \(I\) with List - \(II.\)

List - \(I\)	List - \(II\)
\((a)\) Source of microwave frequency	\((i)\) Radioactive decay on nucleus
\((b)\) Source of infrared frequency	\((ii)\) Magnetron
\((c)\) Source of Gamma Rays	\((iii)\) Inner shell electrons
\((d)\) Source of \(X-\)rays	\((iv)\) Vibration of atoms and molecules
	\((v)\) \(LASER\)
	\((vi)\) \(RC\) circuit

Choose the correct answer from the options given below :