Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NEET2026PhysicsChapterActual

Two simple pendulums are suspended from the same rigid support and start oscillating in phase from their mean positions. They are observed to be in phase again at the mean position for the first time after the shorter pendulum has completed exactly 7 oscillations. What is the ratio of the length of the longer pendulum to that of the shorter pendulum?

Options

  1. A36 : 49
  2. B49 : 36
  3. C7 : 6
  4. D6 : 7

Correct answer

B. 49 : 36

Step-by-step solution

Let T_S and T_L be the time periods of the shorter and longer pendulums respectively, and L_S and L_L be their lengths. For the two pendulums to be in phase again at the mean position for the first time, they must have completed an integer number of oscillations, and the shorter pendulum must have completed exactly one more oscillation than the longer pendulum. Given that the shorter pendulum completes 7 oscillations, the longer pendulum must have completed 7 - 1 = 6 oscillations in the same time interval. Equating

Practice Chapter on Quantrex Academy →

More from Chapter

A solid spherical body of radius R , density , and specific heat capacity s is initially at temperature T₀ . It is placed in a vacuum chamber at absolute zero and cools by emitting 2026A straight canal has motorboats departing from two terminals at opposite ends. The motorboats depart at regular intervals of T minutes in both directions and travel at a constant s 2026A wooden crate is released from rest at the top of a ramp inclined at 37^ to the horizontal. When the ramp is perfectly smooth, the crate reaches the bottom with a speed v . When t 2026A uniform horizontal beam of mass 6 kg and length L is hinged to a vertical wall at one end. The other end is supported by a light inextensible wire attached to the same wall, maki 2026A bullet P of mass 30 g moving with a speed of 200 m/s penetrates a target and comes to rest after travelling a distance of 10 cm inside it. Another bullet Q of mass 20 g moving wi 2026A small block of mass m is placed at the highest point of a smooth fixed sphere of radius R . It is given a horizontal initial speed v₁ such that it slides down the surface. The bl 2026A block of mass 2 kg is projected with an initial speed of 14 m/s on a rough horizontal surface. The coefficient of kinetic friction between the block and the surface is 0.2 . Afte 2026A uniform horizontal circular disc of mass M and radius R is rotating freely about a vertical axis passing through its center at an angular speed of 40 rpm . Two small blocks, each 2026 Full Chapter list All NEET PYQs