The value of the acceleration due to gravity is \(g _{1}\) at a height \(h =\frac{ R }{2}( R =\) radius of the earth) from the surface of the earth. It is again equal to \(g _{1}\) at a depth \(d\) below the surface of the earth. The ratio \(\left(\frac{ d }{ R }\right)\) equals

In an experiment of determine the Young's modulus of wire of a length exactly \(1\; m\), the extension in the length of the wire is measured as \(0.4\,mm\) with an uncertainty of \(\pm 0.02\,mm\) when a load of \(1\,kg\) is applied. The diameter of the wire is measured as \(0.4\,mm\) with an uncertainty of \(\pm 0.01\,mm\). The error in the measurement of Young's modulus \((\Delta Y)\) is found to be \(x \times 10^{10}\,Nm ^{-2}\). The value of \(x\) is \(\left[\right.\) Take \(\left.g =10\,m / s ^{2}\right]\)

The vertical component of the earth's magnetic field is \(6 \times 10^{-5} T\) at any place where the angle of dip is \(37^{\circ}\). The earth's resultant magnetic field at that place will be \(\left(\right.\) Given \(\left.\tan 37^{\circ}=\frac{3}{4}\right)\)

The velocity time graph of a body moving in a straight line is shown in figure.The ratio of displacement to distance travelled by the body in time \(0\) to \(10\,s\) is

The root mean square speed of molecules of a given mass of a gas at \(27^{\circ} C\) and \(1\) atmosphere pressure is \(200\, ms ^{-1}\). The root mean square speed of molecules of the gas at \(127^{\circ} C\) and \(2\) atmosphere pressure is \(\frac{ x }{\sqrt{3}}\, ms ^{-1} .\) The value of \(x\) will be ......\(ms ^{-1} .\)

Two long current carrying conductors are placed parallel to each other at a distance of \(8 \,cm\) between them. The magnitude of magnetic field produced at mid-point between the two conductors due to current flowing in them is \(300 \,\mu T\). The equal current flowing in the two conductors is ...............

The magnifying power of a telescope with tube \(60\; \mathrm{cm}\) is \(5 .\) What is the focal length of its eye piece?......\(cm\)

A cell, shunted by a \(8 \; \Omega\) resistance, is balanced across a potentiometer wire of length \(3 \;  m\). The balancing length is \(2 \; m\) when the cell is shunted by \(4 \; \Omega\) resistance. The value of internal resistance of the cell will be \(\dots \; \Omega .\)

Choose the correct relationship between Poisson ratio \((\sigma)\). bulk modulus \(( K )\) and modulus of rigidity \((\eta)\) of a given solid object:

The graph shows variation of stopping potential \(V_o\) with the frequency \(\nu\) of the incident radiation for three photosensitive metals \(X_1\), \(X_2\) and \(X_3\). Which metal will give out electrons with greater kinetic energy, for the same wavelength of incident radiation?