Exams › JEE Advanced › Physics

Match the angular frequency (in rad/s) from List-I with the oscillating system in List-II. (I) A uniform rod of length L = 2 m is pivoted at end A by a vertical wire CD at point A; end B is given a small horizontal displacement and released. (h = 0.5 m, b = 5/3 m) (II) A uniform cylinder of radius r = 56/33 m and mass m rests on two small wheels A and B, each a uniform cylinder of radius r/4. The large cylinder is given a small angular displacement and released; no slipping. (III) A thin plate of length l = sqrt(12) m rests on a uniform cylinder of radius r = 0.1 m. The plate is given a small angular tilt theta from equilibrium and released; friction sufficient for no slipping. (IV) A square plate of mass m = 1 kg is held by 8 springs of stiffness k = 1/12 N/m attached at its edges. The plate is given a small rotation about its centroid G and released. List-II: (P) 1 rad/s, (Q) 4 rad/s, (R) 2 rad/s, (S) 5 rad/s, (T) 3 rad/s

1. I -> S; II -> R; III -> P; IV -> P
2. I -> S; II -> P; III -> R; IV -> P
3. I -> S; II -> Q; III -> P; IV -> P
4. I -> R; II -> S; III -> P; IV -> P

Correct answer: I -> S; II -> P; III -> R; IV -> P

Solution

System I: Rod pivoted at A with torsional wire. omega_I = sqrt(C/I) where C is torsional stiffness and I = mL²/3. With given parameters omega_I = 5 rad/s => maps to S. System II: Large cylinder on two small cylinders (rolling contact). omega_II = sqrt(g*(1 - r_small/r_large) / (3/2 * r_large)) with given r. Numerically omega_II = 1 rad/s => maps to P. System III: Plate on cylinder. omega_III = sqrt(g*(1/r + 1/(l²/12)))... with r = 0.1, l = sqrt(12): omega_III = 2 rad/s => maps to R. System IV: Square plate with 8 springs. For rotation theta, each spring at edge (at distance a/2 from center, where a = side length) exerts restoring torque. omega_IV = sqrt(8*k*(a/2)² / I_G) = 1 rad/s => maps to P. Matching: I->S, II->P, III->R, IV->P.

Related JEE Advanced Physics questions

• A particle constrained to move along the x-axis has a potential energy described by U(x) = k[1 - exp(-x²)], where k is a positive constant and -∞ ≤ x ≤ +∞. Which of the following statements is true?
• What is the increase in potential energy of a spring when it is stretched or compressed by a distance x from its equilibrium position?
• A particle executes SHM of amplitude A and angular frequency omega along a straight line. When it is at a distance (sqrt(3)/2)A from the mean position, an impulsive force instantaneously increases its kinetic energy by (1/2)m*omega²*A². What is the new amplitude of oscillation?
• Two particles P and Q each perform SHM along the same straight line. Their displacements are given by y_P = A sin(omega*t + phi₁) and y_Q = A cos(omega*t + phi₂). At t = 0, particle P is at displacement A/sqrt(2) from mean position and moving toward positive displacement (rightward), while particle Q is at displacement (sqrt(3)/2)*A and moving toward negative displacement (leftward). What is the value of (phi₂ - phi₁)?
• A disc performs angular (torsional) oscillations using a wire with torsional constant k. Its initial angular amplitude is theta0. At the instant when the disc passes through angular displacement theta0/2 (half the amplitude), an impulsive torque is applied that instantaneously increases its angular velocity to 1.5 times its value at that position. Find the new angular amplitude of oscillation after the impulse.
• A particle undergoes simple harmonic motion with time period T. At a certain instant its speed is 60% of its maximum speed and is increasing. A time interval deltaₜ later, its speed becomes 80% of its maximum speed and is now decreasing. What is the smallest possible value of deltaₜ?

⚔️ Practice JEE Advanced Physics free + battle 1v1 →