A point source of light is placed at the centre of curvature of a hemispherical surface. The source emits a power of \(24\,W\) The radius of curvature of hemisphere is \(10\,cm\) and the inner surface is completely reflecting. The force on the hemisphere due to the light falling on it is \(..........\times 10^{-8}\,N\).

Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by 15 cm length of wire Q is ___________.

\(\left(\mu_0=4 \pi \times 10^{-7} T . m / A \right)\)

In a hypothetical fission reaction \({ }_{92} \mathrm{X}^{236} \rightarrow{ }_{56} \mathrm{Y}^{141}+{ }_{36} \mathrm{Z}^{92}+3 \mathrm{R}\) The identity of emitted particles \((R)\) is _______.

Given below are two statements: Statement \(I\) : The diamagnetic property depends on temperature. Statement \(II\) : The included magnetic dipole moment in a diamagnetic sample is always opposite to the magnetizing field. In the light of given statement, choose the correct answer from the options given below:

A particle starts simple harmonic motion from the mean position. Its amplitude is \(a\) and total energy \(E\). At one instant its kinetic energy is \(3E/4.\) Its displacement at that instant is

Match List \(- I\) with List \(- II\)

List\(-I\) (Layer of atmosphere)	List\(-II\) (Approximate height over earth's surface)
\((A)\) \(F_1\) - Layer	\((I)\) \(10\,km\)
\((B)\) \(D-\) Layer	\((II)\) \(170-190\,km\)
\((C)\) Troposphere	\((III)\) \(100\,km\)
\((D)\) \(E-\)layer	\((IV)\) \(65-75\,km\)

Choose the correct answer from the options given below:

A force is represented by \(\mathrm{F}=a \mathrm{x}^2+\mathrm{bt}^{1 / 2}\). Where \(\mathrm{x}=\) distance and \(\mathrm{t}=\) time. The dimensions of \(\mathrm{b}^2 / \mathrm{a}\) are _______.

A capacitor, \(C_1=6 \mu \mathrm{~F}\) is charged to a potential difference of \(\mathrm{V}_0=5 \mathrm{~V}\) using a 5 V battery. The battery is removed and another capacitor, \(\mathrm{C}_2=12 \mu \mathrm{~F}\) is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges \(\left(q_1\right.\) and \(\left.q_2\right)\) on the capacitors \(C_1\) and \(C_2\) when equilibrium condition is reached.

Each of three blocks \(P\), \(Q\) and \(R\) shown in figure has a mass of \(3 \mathrm{~kg}\). Each of the wire \(A\) and \(B\) has cross-sectional area \(0.005 \mathrm{~cm}^2\) and Young's modulus \(2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}\). Neglecting friction, the longitudinal strain on wire \(B\) is _______ \(\times 10^{-4}\). \(\left(\right.\) Take \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) )

Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass \(=500\, g\), Decay constant \(=20 \,g / s\) then ...... \(s\) time is required for the amplitude of the system to drop to half of its initial value ? \((\ln 2=0.693)\)