If velocity \([V],\) time \([T]\) and force \([F]\) are chosen as the base quantities, the dimensions of the mass will be

A body starts moving from rest with constant acceleration covers displacement \(S_1\) in first \((p-1)\) seconds and \(S_2\) in first \(p\) seconds. The displacement \(S_1+S_2\) will be made in time :

In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of \(\left[M^P L^{\circ} \mathrm{T}^{\mathrm{R}} \mathrm{A}^{\mathrm{S}}\right]\). The value of P and Q are :

A square frame of side \(10\, cm\) and a long straight wire carrying current \(1\, A\) are in the plate of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of \(10\, ms^{-1}\) (see figure). The \(e.m. f\) induced at the time the left arm of the frame is at \(x\, = 10\, cm\) from the wire is .....\(\mu V\)

The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of \(100\, V\). What should nearly be the ratio of their wavelengths ? \(\left( m _{ P }=1.00727\, u , m _{ e }=0.00055 \,u \right)\)

The average energy released per fission for the nucleus of \({ }_{92}^{235} U\) is 190 MeV . When all the atoms of 47 g pure \({ }_{92}^{235} U\) undergo fission process, the energy released is \(\alpha \times 10^{23} MeV\). The value of \(\alpha\) is ___________.
(Avogadro Number \(=6 \times 10^{23}\) per mole)

Mercury is filled in a tube of radius \(2 \mathrm{~cm}\) up to a height of \(30 \mathrm{~cm}\). The force exerted by mercury on the bottom of the tube is _______ \(\mathrm{N}\). (Given, atmospheric pressure \(=10^5 \mathrm{Nm}^{-2}\), density of mercury \(=1.36 \times 10^4 \mathrm{~kg} \mathrm{~m}^3, \mathrm{~g}=10 \mathrm{~ms}^2\), \(\left.\pi=\frac{22}{7}\right)\)

First, a set of \({n}\) equal resistors of \(10\; \Omega\) each are connected in series to a battery of emf \(20\; {V}\) and internal resistance \(10\; \Omega .\) A current \(I\) is observed to flow. Then, the \(n\) resistors are connected in parallel to the same battery. It is observed that the current is increased \(20\) times, then the value of \(n\) is .... .

The reading in the ideal voltmeter \((V)\) shown in the given circuit diagram is _______.