Which of the following expressions corresponds to simple harmonic motion along a straight line, where \(x\) is the displacement and \(a, b, c\) are positive constants?

A galvanometer ( \(G\) ) of \(2 \Omega\) resistance is connected in the given circuit. The ratio of charge stored in \(C_1\) and \(C_2\) is _______.

With rise in temperature, the Young's modulus of elasticity _______.

The resistance of a galvanometer is \(50\, ohm\) and the maximum current which can be passed through it is \(0.002\, A\). What resistance must be connected to it in order to convert it into an ammeter of range \(0 -0.5\, A\) ?....\(ohm\)

If average depth of an ocean is \(4000 \mathrm{~m}\) and the bulk modulus of water is \(2 \times 10^9 \mathrm{Nm}^{-2}\), then fractional compression \(\frac{\Delta V}{V}\) of water at the bottom of ocean is \(\alpha \times 10^{-2}\). The value of \(\alpha\) is ___________(Given, \(\mathrm{g}=10 \mathrm{~ms}^{-2}, \rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}\) )

Two electrons are moving in orbits of two hydrogen like atoms with speeds \(3 \times 10^5 m / s\) and \(2.5 \times 10^5 m / s\) respectively. If the radii of these orbits are nearly same then the possible order of energy states are _________ respectively.

A sphere of mass \(2\,kg\) and radius \(0.5\, m\) is rolling with an initial speed of \(1 \,ms ^{-1}\) goes up an inclined plane which makes an angle of \(30^{\circ}\) with the horizontal plane, without slipping. How low will the sphere take to return to the starting point \(A\) ? (in \(second\))

A metallic rod oflength '\(l\)' is tied to a string oflength \(2l\). and made to rotate with angular speed w on a horizontal table with one end of the string fixed. Ifthere is a vertical magnetic field '\(B\)' in the region, the \(e.m.f.\) induced across the ends of the rod is

Moment of inertia of a body about a given axis is \(1.5\, kg\, m^2\) Initially the body is at rest. In order to produce a rotational kinetic energy of \(1200\, J\), the angular acceleration of \(20\, rad/s^2\) must be applied about the axis of rotation for a duration of ......... \(\sec\).

To light, a \(50\,W , 100\,V\) lamp is connected, in series with a capacitor of capacitance \(\frac{50}{\pi \sqrt{ x }} \mu F\), with \(200 V , 50 Hz AC\) source. The value of \(x\) will be........

A current of \(1\,A\) is flowing on the sides of an equilateral triangle of side \(4.5\times10^{-2}\,m\) . The magnetic field at the centre of the triangle will be