Archives: Questions

Consider the diameter of a spherical object being measured with the help of a Vernier callipers. Suppose its 10 Vernier Scale Divisions (V.S.D.) are equal to its 9 Main Scale Divisions (M.S.D.). The least division in the M.S. is 0.1 cm and the zero of V.S. is at $x=0.1$ cm when the jaws of Vernier … Read more

A balloon is made of a material of surface tension S and its inflation outlet (from where gas is filled in it) has small area A. It is filled with a gas of density $\rho$ and takes a spherical shape of radius R. When the gas is allowed to flow freely out of it, its … Read more

In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency $\omega(t)$ and average amplitude $A(t)$ of the system change with time t. Which one of the following options schematically depicts these changes … Read more

A uniform rod of mass 20 kg and length 5 m leans against a smooth vertical wall making an angle of $60^{\circ}$ with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is (Take $g=10~m/s^{2}$)

Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of $60~km/h$ in the direction X to Y notices that a bus goes past her every 30 minutes in the direction of her motion, and … Read more

The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constant $K_{1}$ and $K_{2}$ with thickness $\frac{3}{8}d$ and $\frac{d}{2}$ respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If $K_{1}=1.25~K_{2}$, the value of $K_{1}$ is:

Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity 2K while that in the middle has thermal conductivity K. The left end of the combination is maintained at temperature 3T and the right end at T. The rods are thermally insulated from … Read more

A model for quantized motion of an electron in a uniform magnetic field B states that the flux passing through the orbit of the electron is $n(h/e)$ where n is an integer, h is Planck’s constant and e is the magnitude of electron’s charge. According to the model, the magnetic moment of an electron in … Read more

The Sun rotates around its centre once in 27 days. What will be the period of revolution if the Sun were to expand to twice its present radius without any external influence? Assume the Sun to be a sphere of uniform density.

To an ac power supply of 220 V at 50 Hz, a resistor of $20~\Omega$, a capacitor of reactance $25~\Omega$ and an inductor of reactance $45~\Omega$ are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage is, respectively