The engine of a train moving with speed \(10\,ms ^{-1}\) towards a platform sounds a whistle at frequency \(400\,Hz\). The frequency heard by a passenger inside the train is \(........\,Hz\) (neglect air speed. Speed of sound in air \(330\,ms ^{-1}\) )

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\(^2\))

A solid disc of radius \(20 \,{cm}\) and mass \(10\, {kg}\) is rotating with an angular velocity of \(600\, {rpm}\), about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc at rest in \(10\, {s}\, ......\, \pi \times \,10^{-1}\, {Nm}\).

A \(\sqrt{34}\,m\) long ladder weighing \(10\,kg\) leans on a frictionless wall. Its feet rest on the floor \(3\,m\) away from the wall as shown in the figure. If \(F_{f}\) and \(F_{w}\) are the reaction forces of the floor and the wall, then ratio of \(F _{ a } / F _{f}\) will be: (Use \(\left.g=10\,m / s ^{2}\right)\)

An engine approaches a hill with a constant speed. When it is at a distance of \(0.9\, km\), it blows a whistle whose echo is heard by the driver after \(5\, seconds\). If the speed of sound in air is \(330\, m/s\), then the speed of the engine is .... \(m/s\)

A plane electromagnetic wave travels in free space along the \(x -\) direction. The electric field component of the wave at a particular point of space and time is \(E =6\; Vm^{-1}\) along \(y -\) direction. Its corresponding magnetic filed component, \(B\) would be

A solid cylinder of mass \(m\) is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is: [The coefficient of static friction, \(\mu_{ s },\) is \(\left.0.4\right]\)

At some instant, a radioactive sample \(S_1\) having an activity \(5\,\mu Ci\)  has twice the number of nuclei as another sample \(S_2\)  which has an activity of  \(10\,\mu Ci.\)  The halflives of \(S_1\)  and  \(S_2\) are

A capacitor of reactance \(4 \sqrt{3} \Omega\) and a resistor of resistance \(4 \Omega\) are connected in series with an ac source of peak value \(8 \sqrt{2} \mathrm{~V}\). The power dissipation in the circuit is _______ \(W\).

The density and breaking stress of a wire are \(6 \times\) \(10^4 \mathrm{~kg} / \mathrm{m}^3\) and \(1.2 \times 10^8 \mathrm{~N} / \mathrm{m}^2\) respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is \(\frac{1^{\text {rd }}}{3}\) of the value on the surface of earth. The maximum length of the wire with breaking is _______ \(\mathrm{m}\) (take, \(\mathrm{g}=\) \(\left.10 \mathrm{~m} / \mathrm{s}^2\right)\)

In the circuit shown in the figure, the total charge in \(750\, \mu C\) and the voltage across capacitor \(C _{2}\) is \(20\, V\). Then the charge on capacitor \(C _{2}\) is\(....\mu C\)