Physics and Chemistry Exam Instructions

In a series LCR circuit, the rms voltage across the resistor is 30V and across the capacitor is 90V. If the applied voltage is $50\sqrt{2} \sin(\omega t)$, what is the peak voltage across the inductor?

A small ball of mass m is suspended from the ceiling by a string of length L. The ball moves along a horizontal circle at a constant angular velocity $ \omega $. What is the torque about the center (O) of the horizontal circle?

Three point charges, q, -2q, and q are placed along the x-axis at x = -a, 0, and a, respectively. If $a \to 0$ and $q \to \infty$ while $qa^2 = Q$ remains finite, what is the electric field at a point P at a distance x (where x >> a) from x = 0?

Two convex lenses (L1 and L2) with equal focal length f are placed a distance of $f/2$ apart. An object is placed a distance 4f to the left of L1. Where is the final image located?

A charged particle moves with a velocity $ \vec{v} = v_1 \hat{i} + v_2 \hat{j} $ in a magnetic field $ \vec{B} $ and experiences a force $ \vec{F} = F_1 \hat{i} + F_2 \hat{j} $. Assuming $ v_1 $, $ v_2 $, $ F_1 $, and $ F_2 $ are all constants, which of the following could represent the magnetic field $ \vec{B} $?

Two straight conducting plates form an angle $ \theta $ where their ends are joined. A conducting bar in contact with the plates forms an isosceles triangle. At t=0 the bar starts moving with constant velocity $ \vec{v} $. A magnetic field B points out of the page. What is the magnitude of the emf induced at t = 1 second?

A body floats with 1/n of its volume outside of water. If the body is pushed a height h inside the water and released, what is the time it takes to reach the surface?

A small sphere of mass m and radius r rolls without slipping down a smooth, large hemispherical bowl of radius R. If the sphere starts from rest, what is the total kinetic energy of the sphere at the lowest point A of the bowl? (Given: moment of inertia of sphere = $ \frac{2}{5}mr^2 $)

The internal energy of a thermodynamic system is given by $U = aS^{4/3}V^{-1/3}$, where S is entropy, V is volume, and a is a constant. What are the units of the constant 'a'?

A particle of mass m moves in one dimension under the action of a conservative force whose potential energy is $U(x) = \frac{ \alpha x}{x^2 + \beta^2} $, where $ \alpha $ and $ \beta $ are dimensional parameters. The angular frequency of oscillation ($ \omega $) is proportional to

A charge Q is placed at the center of a cube with sides of length a. What is the total electric flux through all six surfaces of the cube?

A 2V cell is connected across points A and B in the given circuit. Assume that the resistance of each diode is zero in forward bias and infinite in reverse bias. What is the current supplied by the cell?

A metal plate with area $10^{-2} m^2$ rests on a 2 x $10^{-3}m$ thick layer of castor oil having a coefficient of viscosity of 1.55 Ns/m². What horizontal force is required to move the plate at a uniform speed of 3 x $10^{-2} m/s$

A convex lens is placed above an empty tank. The mark at the bottom of the tank appears 36 cm above the lens, though the tanks is really a distance of 45cm away. When liquid poured in the tank reaches a depth of 40cm, the mark appears to be 48 cm above the lens. Find the index of refraction for the liquid.

In the given network of AND and OR gates, what is the output Q, assuming n is even?

In a cylindrical vessel of height H, water is filled. A hole is made at height z from the bottom. What is the z-value for which the water's range, R, is maximum?

In a single-slit diffraction experiment, the slit is illuminated by light of two wavelengths $ \lambda_1 $ and $ \lambda_2 $. It is obeserved that the 2nd order diffraction mimimum for $ \lambda_1 $ coincides with the 3rd order minimum for $ \lambda_2 $. Then,

Consider a circuit where a voltage source $E_0$ with internal resistance r is connected across terminals A and B as shown. What value of R will maximize power generated by this circuit?

Identify the correct statement regarding the characteristics of nuclear binding energy:

What force F is required to start moving this 10kg block in the figure, if the force F is applied at an angle of 60 degrees as shown, and the coefficient of static friction $ \mu_s $ is 0.6?

Light of wavelength 6000 angstroms is incident on a thin glass plate with index of refraction 1.5 such that angle of refraction is 60 degrees. What is the thinnest, non-zero thickness for the glas plate to produce a dark fringe (destructive interference)?

A satellite of mass m rotates around the earth in a circular orbit of radius R. If the angular momentum of the satellite is J, then its kinetic energy (K) and the total energy (E) of the satellite are:

In a series LCR circuit, the variation of impedance Z with the source frequency is shown in the figure. Based on the graph, which of the following statements is true?

The electric field of a plane electromagnetic wave in a medium is given by $ E(x, y, z, t) = E_0 \hat{n}e^{ik[(x+y+z)-ct]} $, where c is the speed of light in free space. What is true of the propagation vector $ \hat{n} $ and the wave's speed in the medium v given that E is polarized in the x-z plane?

Monochromatic light with wavelength 4770Å illuminates metals A, B, C, and D with work functions of 4.2 eV, 3.7 eV, 3.2 eV, and 2.3 eV respectively. What metal(s) emit electrons?

Consider the integral form of Gauss' Law in electrostatic $ \oint \vec{E} \cdot d\vec{s} = \frac{Q}{\epsilon_0} $. Which statements are correct?

A uniform rod AB of length 1m and mass 4kg is sliding along mutually perpendicular frictionless walls OX and OY. The velocities of the two ends of the rod A and B are 3 m/s and 4 m/s respectively. Which statement(s) are correct?

Which one among the following is the incorrect statement

Among the following statements related to equilibrium constant and rate constant of a single step chemical reaction, then identify the true equation

Equal volumes of aqueous solutions of 0.1(M) HCl and 0.2(M) $H_2SO_4$ are mixed. What is the concentration of $H^+$ ions in the resulting solution?

What is the correct boiling point order of the given solutions?

After the emission of a $ \beta $-particle followed by an $ \alpha $-particle from $ _{83}^{211}Bi $, determine number of neutrons in the atom is:

Which hydrogen like species will have the same radii as first Bohr orbit of hydrogen atom?

Consider a first order reaction with a rate constant of k. Which is proportional to tangent of plot for reactants with time?