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 \(10\, {s}\, ......\, \pi \times \,10^{-1}\, {Nm}\).

Consider a moving coil galvanomenter (MCG):
A. The torsional constant in moving coil galvanometer has dimentions \(\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]\)
B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity.
C. If we increase number of turns \((\mathrm{N})\) to its double \((2 \mathrm{~N})\), then the voltage sensitivity doubles.
D. MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer.
E. Current sensitivity of MCG depends inversely on number of turns of coil.
Choose the correct answer from the options given below:

At an angle of \(30^{\circ}\) to the magnetic meridian, the apparent dip is \(45^{\circ} .\) Find the true dip :

A body of mass 2 kg is moving along x -direction such that its displacement as function of time is given by \(x ( t )=\alpha t ^2+\beta t +\gamma m\), where \(\alpha=1 m / s ^2\), \(\beta=1 m / s\) and \(\gamma=1 m\). The work done on the body during the time interval \(t =2 s\) to \(t =3 s\), is _________ J.

A projectile of mass \(M\) is fired so that the horizontal range is \(4\, km\). At the highest point the projectile explodes in two parts of masses \(M/4\) and \(3M/4\) respectively and the heavier part starts falling down vertically with zero initial speed. The horizontal range (distance from point of firing) of the lighter part is .................. \(\mathrm{km}\)

In a meter bridge, the wire of length \(1\, m\) has a nonuniform cross-section such that, the variation \(\frac{{dR}}{{d\ell }}\) of its resistance \(R\) with length \(\ell \) is \(\frac{{dR}}{{d\ell }} \propto \frac{1}{{\sqrt \ell  }}\) Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point \(P\). What is the length \(AP\) ? ................ \(m\)

The energy of a system is given as \(\mathrm{E}(\mathrm{t})=\alpha^3 \mathrm{e}^{-\beta t}\), where t is the time and \(\beta=0.3 \mathrm{~s}^{-1}\). The errors in the measurement of \(\alpha\) and \(t\) are \(1.2 \%\) and \(1.6 \%\), respectively. At \(t=5 \mathrm{~s}\), maximum percentage error in the energy is :

If \(L , C\) and \(R\) are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time?

Water fall from a \(40\,m\) high dam at the rate of \(9 \times 10^{4}\,kg\) per \(hour\). Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of \(100\,W\) lamps, that can be lit, is (Take \(\left.g=10\,ms ^{-2}\right)\)