Young's modulus experiment is performed on a steel wire of \(1 \mathrm{~m}\) length and \(8 \mathrm{~mm}\) diameter. The mass required to be added in the experiment to produce \(5 \mathrm{~mm}\) elongation of the wire is \(\left(Y_{\text {steel }}=2 \times 10^9 \mathrm{Nm}^{-2}, g=10 \mathrm{~m} / \mathrm{s}^2\right)\)

Which of the following is the unit of mobility of a electron in a conductor?

Consider a wheel rotating around a fixed axis. If the rotation angle \(\theta\) varies with time as \(\theta=a t^2\), then the total acceleration of a point \(A\) on the rim of the wheel is \((v\) being the tangential velocity)

Two wooden blocks of masses \(M\) and \(m\) are placed on a smooth horizontal surface as shown in figure. If a force \(P\) is applied to the system as shown in figure such that the mass \(m\) remains stationary with respect to block of mass \(M\), then the magnitude of the force \(P\) is

Conservative forces are defined as the force for which,

One junction of a certain thermoelectric couple is at a fixed temperature \(T_r\) and the other junction is at temperature \(T\). The thermo-electromotive force for this is expressed by \(E=k\left(T-T_r\right)\left[T_0-\frac{1}{2}\left(T+T_r\right)\right]\). At temperature \(T=\frac{1}{2} T_0\), the thermoelectric power is

A planet is moving in a circular orbit. It completes $2$ revolutions in $360 \mathrm{days}$. What is its angular frequency?

Magnetic field induction at the centre of a circular coil of radius \(5 \mathrm{~cm}\) and carrying a current \(0.9 \mathrm{~A}\) is (in SI units) \(\left(\varepsilon_0=\right.\) absolute permittivity of air in SI units, velocity of light \(=3 \times 10^8 \mathrm{~ms}^{-1}\) )

A bullet enters a wooden block with velocity \(120 \mathrm{~m} / \mathrm{s}\). The bullet travels \(1.5 \mathrm{~s}\) in the block before its velocity reduces to zero due to resistance force which is proportional to the square root of the velocity. The distance travelled by the bullet in the wooden block is

In the pulley system, the mass of ball is 1.2 times greater than the mass of the rod. The length of the rod is \(50 \mathrm{~cm}\). The ball is set on the same level as the lower end of the rod and then released. What is the acceleration of the rod with which it comes down? Assume the pulleys and threads are massless and friction force is neglected. (Use, \(g=10 \mathrm{~m} / \mathrm{s}^2\) )

Match the following table. \begin{array}{|c|c|c|c|} \hline & List-I & & List-II \ \hline A. & \begin{array}{l}\text { Michelson-Morley } \ \text { experiment }\end{array} & I. & \begin{array}{l}\text { The existence of } \ \text { anti-matter }\end{array} \ \hline B. & \begin{array}{l}\text { Stern-Gerlach } \ \text { experiment }\end{array} & II. & \begin{array}{l}\text { The existence of } \ \text { de-Broglie matter waves }\end{array} \ \hline C. & \begin{array}{l}\text { Davisson-Germer } \ \text { experiment }\end{array} & III. & Electrons have spins \ \hline D. & \begin{array}{l}\text { Anderson discovery } \ \text { of positron }\end{array} & \mathrm{IV}. & \begin{array}{l}\text { The non-existence of } \ \text { ether }\end{array} \ \hline \end{array} \(\begin{array}{llll}A & B & C & D\end{array}\)

The equation of trajectory of a projectile is \(y=10 x-\left(\frac{5}{9}\right) x^2\). If we assume \(g=10 \mathrm{~ms}^{-2}\), the range of projectile (in metre) is

Which of the following pairs has same dimensions?