Sample Quiz

A uniform conducting wire of length 12a and resistance R is wound up as a current-carrying coil in the shape of,
(i) an equilateral triangle of side ‘a’
(ii) A square of side ‘a’
The magnetic dipole moments of the coil in each case respectively are:

A particle of mass ‘m’ is projected with a velocity \(v=k V_{e}(k<1)\) from the surface of the earth. \(\left(V_{e}=\right. escape  velocity)\)
The maximum height above the surface reached by the particle is:

A series LCR circuit containing a 5.0 H inductor, 80μF capacitor, and 40Ω resistor is connected to a 230V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be:

A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle ‘\(\theta\)’ to the horizontal, the maximum height attained by it equals 4 R. The angle of projection, \(\theta\), is then given by :

Two conducting circular loops of radii \(R_{1}\) and \(R_{2}\) are placed in the same plane with their centers coinciding. If \(\mathrm{R}_{1}>>\mathrm{R}_{2}\), the mutual inductance M between them will be directly proportional to:

Twenty-seven drops of the same size are charged at 220 V each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

A uniform rod of length 200 cm and mass of 500 g is balanced on a wedge placed at the 40 cm mark. A mass of 2 kg is suspended from the rod at 20 cm and another unknown mass ‘m’ is suspended from the rod at 160 cm mark as shown in the figure. Find the value of ‘m’ such that the rod is in equilibrium. \(\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)\)

A point object is placed at a distance of 60 cm from a convex lens of a focal length of 30 cm. If a plane mirror was put perpendicular to the principal axis of the lens and at a distance of 40 cm from it, the final image would be formed at a distance of

A car starts from rest and accelerates at \(5 \mathrm{~m} / \mathrm{s}^{2}\). At \(\mathrm{t}=4 \mathrm{~s}\), a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at \(\mathrm{t}=6 \mathrm{~s}\)?

(Take \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\))

For the given circuit, the input digital signals are applied at terminals A, B, and C. What would be the output at terminal y?