Comprehensive Science Exam Guide

A coil with a diameter of 1 mm and 35 turns is rotated $180^\circ$ in 0.1 seconds in a 100 Gauss external uniform magnetic field. What is the average induced EMF in the coil?

In an AC circuit, the instantaneous EMF (e) and current (i) are given by $e = E_0 \sin(\omega t)$ and $i = I_0 \sin(\omega t + \phi)$, respectively. What is the average power in the circuit over one complete cycle?

A long straight wire of radius a carries a steady current I uniformly distributed across its cross-section. What is the ratio of the magnetic fields B and B' at radial distances of $a/2$ and $4a$ from the axis of the wire, respectively?

In the given circuit, what is the power dissipated across the $4 \Omega$ resistor?

Three resistors, $P$, $Q$, and $R$, each with a value of $4 \Omega$, and an unknown resistor $S$ form the four arms of a Wheatstone bridge. To balance the bridge, a $6 \Omega$ resistor is connected in parallel with $S$. What is the value of $S$?

In the illustrated circuit, when points $P$ and $M$ are connected to a DC voltage source, the current through the $6 \Omega$ resistor is 1 Ampere. What is the potential difference between points $M$ and $N$?

A wire with a resistance of 24 ohms per meter is bent to form a complete circle with a radius of 10 cm. What is the resistance between its two diametrically opposite points, $A$ and $B$?

A capacitor is charged by a battery. The battery is then removed, and another identical uncharged capacitor is connected in parallel. How does the charge on the first capacitor change?

The oscillation of a body on a smooth horizontal surface is represented by $X = A \sin(\omega t)$, where X is the displacement at time t, and $\omega$ is the angular frequency. Which graph correctly shows the variation of acceleration ('a') with time ('t')?

The efficiency of a Carnot engine does NOT depend on which of the following?

At what temperature is the RMS speed of neon gas atoms equal to the RMS speed of $NH_3$ molecules at $17^\circ C$? (Molar mass of Neon = 20 g/mol)

A container with a volume of 100 $cm^3$ contains 0.1 moles of hydrogen gas and 0.2 moles of argon gas. What is the pressure of the system at 200 K?

Assertion: A spaceship is likely to catch fire while entering Earth's atmosphere.

A moving block of mass m collides with another stationary block with a mass of 2m. After the collision, the lighter block comes to rest. What is the coefficient of restitution (e)?

A mass m is attached to a thin wire and whirled in a vertical circle. When is the wire most likely to break?

For a convex lens forming a real image, which graph correctly represents the relationship between $(|u| + |v|)$ and $|u|$ or $|v|$?

A block of mass m is moving with an initial velocity $u$ toward a stationary spring with stiffness constant k, attached to a wall. What is the compression of the spring when the block's speed is halved? (Assume the surface is frictionless)

The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is $I_0$. What is the moment of inertia about an axis passing through one of its ends and perpendicular to its length?

A hollow sphere (mass 'm' and radius 'R') rolls down an incline of angle '$\theta$' without slipping and then slips down the incline without rolling. What is the ratio of the accelerations in the two cases?

A body of mass 60 g experiences a gravitational force of 3.0 N when placed at a particular point. What is the magnitude of the gravitational field intensity at that point?

When a block of mass M suspended by a long wire of length L, the length of the wire becomes (L+l). What is the elastic potential energy stored in the extended wire?