The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest Young's modulus?

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

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by \(0.02 \%\) is ______ \(\mathrm{m}\). (Take density of sea water \(=10^3 \mathrm{kgm}^{-3}\), Bulk modulus of rubber \(=9 \times 10^8 \mathrm{Nm}^{-2}\), and \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) )

An excited \(He^+\) ion emits two photons in succession, with wavelengths \(108.5\, nm\) and \(30.4\, nm\), in making a transition to ground state. The quantum number \(n\), corresponding to its initial excited state is \(n=........\) (for photon of wavelength \(\lambda \), energy \(E = \frac{{1240\,eV}}{{\lambda \,(in\,nm)}}\))

Given below are two statements: One is labelled as Assertion \((A)\) and other is labelled as Reason \((R)\). Assertion \((A)\) : Time period of oscillation of a liquid drop depends on surface tension \((S)\), if density of the liquid is \(p\) and radius of the drop is \(r\), then \(T = k \sqrt{ pr ^{3} / s ^{3 / 2}}\) is dimensionally correct, where \(K\) is dimensionless. Reason \((R)\): Using dimensional analysis we get \(R.H.S.\) having different dimension than that of time period. In the light of above statements, choose the correct answer from the options given below.

A spherically symmetric charge distribution is characterised by a charge density having the following variations \(\rho (r)\, = \,{\rho _0}\left( {1 - \frac{r}{R}} \right)\) for \(r < R\) \(\rho (r)\,=\,0\) for \(r\, \ge \,R\) Where \(r\) is the distance from the centre of the charge distribution \(\rho _0\) is a constant. The electric field at an internal point \((r < R)\) is

In a nuclear fission process, a high mass nuclide \((A \approx 236)\) with binding energy \(7.6\  \mathrm{MeV} /\) Nucleon dissociated into middle mass nuclides \((A \approx 118)\), having binding energy of \(8.6 \ \mathrm{MeV} / \mathrm{Nucleon}\). The energy released in the process would be \(\mathrm{MeV}\).

The acceleration due to gravity at height \(h\) above the earth if \(h \ll R\) (radius of earth) is given by

An object is placed at a distance of \(12\,cm\) in front of a plane mirror. The virtual and erect image is formed by the mirror. Now the mirror is moved by \(4\,cm\) towards the stationary object. The distance by which the position of image would be shifted, will be:

Two capacitors \(C_1\) and \(C_2\) are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are \(U_1\) and \(U_2\), respectively. Which of the given statements is true?

In Young's double slit experiment, two slits \(S_1\) and \(S_2\) are ' \(d\) ' distance apart and the separation from slits to screen is \(D\) (as shown in figure). Now if two transparent slabs of equal thickness \(0.1\,mm\) but refractive index \(1.51\) and \(1.55\) are introduced in the path of beam \((\lambda=4000 \mathring A)\) from \(S_1\) and \(S_2\) respectively. The central bright fringe spot will shift by  \(..........\) number of fringes.

A train moves towards a stationary observer with speed \(34\, m/s\). The train sounds a whistle and its frequency registered by the observer is \(f_1\). If the speed of the train is reduced to \(17\, m/s\), the frequency registered is \(f_2\). If speed of sound is \(340\, m/s\), then the ratio \(f_1/f_2\) is

White light is passed through a double slit and interference is observed on a screen \(1.5 \,{m}\) away. The separation between the slits is \(0.3 \,{mm}\). The first violet and red fringes are formed \(2.0 \,{mm}\) and \(3.5\, {mm}\) away from the central white fringes. The difference in wavelengths of red and voilet light is \(.... \,{nm} .\)