An object with mass 500 g moves along x -axis with speed \(v=4 \sqrt{x} \mathrm{~m} / \mathrm{s}\). The force acting on the object is :

The maximum potential energy of a block executing simple harmonic motion is \(25\,J\). A is amplitude of oscillation. At \(A / 2\), the kinetic energy of the block is \(...............\)

A paramagnetic substance in the form of a cube with sides \(1\, cm\) has a magnetic dipole moment of \(20 \times 10^{-6}\, J/T\) when a magnetic intensity of \(60 \times 10^3\, A/m\) is applied. Its magnetic susceptibility is

Two wavelengths \(\lambda_1\) and \(\lambda_2\) are used in Young's double slit experiment \(\lambda_1=450 \mathrm{~nm}\) and \(\lambda_2=650 \mathrm{~nm}\). The minimum order of fringe produced by \(\lambda_2\) which overlaps with the fringe produced by \(\lambda_1\) is \(n\). The value of \(n\) is _________.

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

A constant voltage is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be

Electric field in a certain region is given by \(\overrightarrow{ E }=\left(\frac{ A }{ x ^2} \hat{ i }+\frac{ B }{ y ^3} \hat{ j }\right)\). The \(SI\) unit of \(A\) and \(B\) are

Calculate the value of mean free path \((\lambda)\) for oxygen molecules at temperature \(27^{\circ}\, C\) and pressure \(1.01 \times 10^{5} \,Pa\). Assume the molecular diameter \(0.3 \,nm\) and the gas is ideal. \(\left( k =1.38 \times 10^{-23}\, J\,K ^{-1}\right)\) (in \(nm\))

Substance \(A\) has atomic mass number \(16\) and half life of \(1\) day. Another substance \(B\) has atomic mass number \(32\) and half life of \(\frac{1}{2}\) day. If both \(A\) and \(B\) simultaneously start undergo radio activity at the same time with initial mass \(320\,g\) each, how many total atoms of \(A\) and \(B\) combined would be left after \(2\) days \(.........\times 10^{24}\)

A particle performs simple harmonic motion with a period of \(2\) second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is \(\frac{1}{ a } s .\) The value of \('a'\) to the nearest integer is.........

An astronaut takes a ball of mass \(m\) from earth to space. He throws the ball into a circular orbit about earth at an altitude of \(318.5 \mathrm{~km}\). From earth's surface to the orbit, the change in total mechanical energy of the ball is \(x \frac{\mathrm{GM}_e \mathrm{~m}}{21 R_e}\). The value of \(x\) is _______. (take \(R_{\mathrm{e}}=6370 \mathrm{~km}\) )

When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on