A steel wire with mass per unit length \(7.0 \times 10^{-3}\,kg\,m ^{-1}\) is under tension of \(70\,N\). The speed of transverse waves in the wire will be \(.........m/s\)

The figure given below shows an \(LCR\) series circuit with two switches \(S_1\) and \(S_2\). When switch \(S_1\) is closed keeping \(S_2\) open, the phase difference \((\phi)\) between the current and source voltage is \(30°\) and phase difference is \(60°\) when \(S_2\) is closed keeping \(S_1\) open. The value of \((3L_1 - L_2)\) is _______ H.

A plane is inclined at an angle \(\alpha  = 30^o\) with respect to the horizontal. A particle is projected with a speed \(u = 2\,ms^{-1},\) from the base of the plant, making an angle \(\theta = 15^o\) with respect to the plane as shown in the figure. The distance from the base at which the particle hits the plane is close to  ........ \(cm\) (Take \(g = 10\,ms^2\) )

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 \(..........\times 10^{-8}\,N\).

In an electric circuit, a cell of certain emf provides a potential difference of \(1.25\, {V}\) across a load resistance of \(5\, \Omega .\) However, it provides a potential difference of \(1\, {V}\) across a load resistance of \(2\, \Omega\). The \(emf\) of the cell is given by \(\frac{x}{10} v\). Then the value of \(x\) is ..... .

A disc with a flat small bottom beaker placed on it at a distance \(R\) from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity \(\omega\). The coefficient of static friction between the bottom of the beaker and the surface of the disc is \(\mu\). The beaker will revolve with the disc if 

A \(600\,pF\) capacitor is charged by \(200\,V\) supply. It is then disconnected from the supply and is connected to another uncharged \(600\,pF\) capacitor. Electrostatic energy lost in the process is \(.........\,\mu J\).

At any instant the velocity of a particle of mass \(500\,g\) is \(\left(2 t \hat{ i }+3 t ^2 \hat{ j }\right)\,ms ^{-1}\). If the force acting on the particle at \(t=1 s\) is \((\hat{i}+x \hat{j}) N\). Then the value of \(x\) will be:

A particle of mass \(m\) moves in a circular orbit in a central potential field \(U\left( r \right) = \frac{1}{2}k{r^2}\). If Bohr’s quantization conditions are applied, radii of possible orbits and energy levels vary with quantum number \(n\) as

The angular speed of truck wheel is increased from \(900\, rpm\) to \(2460\, rpm\) in \(26\) seconds. The number of revolutions by the truck engine during this time is (Assuming the acceleration to be uniform).

The position-time graphs for two students \(A\) and \(B\) returning from the school to their homes are shown in figure \((A)\) \(A\) lives closer to the school \((B)\) \(B\) lives closer to the school \((C)\) \(A\) takes lesser time to reach home \((D)\) \(A\) travels faster than \(B\) \((E)\) \(B\) travels faster than \(A\) Choose the correct answer from the options given below :