An inductor \((L = 0.03\;H)\) and a resistor \((R = 0.15 k\Omega )\) are connected in series to a battery of \(15\;V\) \(EMF\) in a circuit shown below. The key \(K_1\) has been kept closed for a long time. Then at \(t = 0\), \(K_1\) is opened and key \(K_2\) is closed simultaneously. At \(t = 1 \;ms\), the current in the circuit will be ........... \(mA\). (\({e^5} \cong 150)\)

A car moving with a speed of \(54\) km/h takes a turn of radius \(20\) m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take \(g=10\) m/s\(^2\))

One of the two small circular coils, (none of them having any self- inductance) is suspended with a \(V-\) shaped copper wire, with plane horizontal. The other coil is placed just below the first one with plane horizontal. Both the coils are connected in series with a \(dc\) supply. The coils are found to attract each other with a force. Which one of the following statements is incorrect ?

A body of mass \(m\)  starts moving from rest along \(x-\) axis so that its velocity varies as \(v = a\sqrt s\) where \(a\) is a constant and \(s\)  is the distance covered by the body. The total work done by all the forces acting on the body in the first second after the start of the motion is

A player caught a cricket ball of mass \(150 \mathrm{~g}\) moving at a speed of \(20 \mathrm{~m} / \mathrm{s}\). If the catching process is completed in \(0.1 \mathrm{~s}\), the magnitude of force exerted by the ball on the hand of the player is _______.

A body of mass \(1 kg\) begins to move under the action of a time dependent force \(\vec{F}=\left(t \hat{i}+3 t^2 \hat{ j }\right) N\). where \(\hat{i}\) and \(\hat{j}\) are the unit vectors along \(x\) and \(y\) axis. The 10.Power developed by above force, at the time \(t=2 s\). will be \(..............W\).

One end of a massless spring of spring constant \(k\) and natural length \(l_{0}\) is fixed while the other end is connected to a small object of mass \(m\) lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity \(\omega\) about an axis passing through fixed end, then the elongation of the spring will be

A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample is _______.

In a microscope of tube length 10 cm two convex lenses are arranged with focal length of 2 cm and 5 cm . Total magnification obtained with this system for normal adjustment is \((5)^{ k }\). The value of k is _________

A parallel plate capacitor is formed by two plates each of area \(30 \pi\, cm ^{2}\) separated by \(1\, mm\). A material of dielectric strength \(3.6 \times 10^{7} \,Vm ^{-1}\) is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is \(7 \times 10^{-6}\, C\), the value of dielectric constant of the material is \(\left\{ Use : \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} Nm ^{2} C ^{-2}\right\}\)

A geostationary satellite is orbiting around an arbitary planet \(^{\prime} P ^{\prime}\) at a height of \(11 R\) above the surface of \(^{\prime} P ^{\prime} ,\) \(R\) being the radius of \(^{\prime} P .^{\prime}\) The time period of another satellite in hours at a height of \(2R\) from the surface of \(^{\prime} P ^{\prime}\) is \(........\).\(^{\prime} P ^{\prime}\) has the time period of \(24\, hours.\)

A \(2 \mathrm{~kg}\) brick begins to slide over a surface which is inclined at an angle of \(45^{\circ}\) with respect to horizontal axis. The co-efficient of static friction between their surfaces is _______.

The amount of work done to break a big water drop of radius ' \(R\) ' into 27 small drops of equal radius is 10 J . The work done required to break the same big drop into 64 small drops of equal radius will be