A physical quantity \(p\) is described by the relation \(p\, = a^{1/2}\, b^2\, c^3\, d^{-4}\) If the relative errors in the measurement of \(a, b, c\) and \(d\) respectively, are \(2\% , 1\%, 3\%\) and \(5\%\), then the relative error in \(P\) will be ........... \(\%\)

A charged particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charged particle increases to \(4\) times its initial value. What will be the ratio of new radius to the original radius of circular path of the charged particle

A plane electromagnetic wave is moving in free space with velocity \(c =3 \times 10^8 m / s\) and its electric field is given as \(\overrightarrow{ E }=54 \sin ( kz -\omega t ) \hat{ j } V / m\), where \(\hat{j}\) is the unit vector along \(y\)-axis. The magnetic field vector \(\overrightarrow{ B }\) of the wave is :

A body travels \(102.5 \mathrm{~m}\) in \(\mathrm{n}^{\text {th }}\) second and \(115.0 \mathrm{~m}\) in \((n+2)^{\text {th }}\) second. The acceleration is what?

Given below are two statements: One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\): If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude. Reason \(R \): At equator, the direction of acceleration due to the gravity is towards the center of earth. In the light of above statements, choose the correct answer from the options given below

A cubic block of mass \(m\) is sliding down on an inclined plane at \(60^{\circ}\) with an acceleration of \(\frac{\mathrm{g}}{2}\), the value of coefficient of kinetic friction is

The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have _________.

A cylindrical vessel of cross-section \(A\) contains water to a height \(h\) . There is a hole in the bottom of radius \('a'\) . The time in which it will be emptied is

An infinite plane sheet of charge having uniform surface charge density \(+\sigma_5 \mathrm{C} / \mathrm{m}^2\) is placed on \(\mathrm{x}-\mathrm{y}\) plane. Another infinitely long line charge having uniform linear charge density \(+\lambda_e \mathrm{C} / \mathrm{m}\) is placed at \(z=4 \mathrm{~m}\) plane and parallel to \(y\)-axis. If the magnitude values \(\left|\sigma_s\right|=2\left|\lambda_{\mathrm{e}}\right|\) then at point \((0,0,2)\), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is \(\pi \sqrt{\mathrm{n}}: 1\). The value of \(n\) is _______.

The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is ___________ cm.