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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

A pendulum having a bob of mass m hangs in a ship that is sailing along the equator from east to west. When the ship is stationary with respect to the water, the tension in the string is T₀ . The angular speed of the earth's rotation is and the radius of the earth is R . If the ship sails at a speed v , what is the approximate tension in the string?

Options

  1. AT₀ + m v
  2. BT₀ + 2 m v
  3. CT₀ - m v
  4. DT₀ - 2 m v

Correct answer

B. T₀ + 2 m v

Step-by-step solution

Let the true acceleration due to gravity be g . The earth rotates from west to east with an angular speed . When the ship is stationary with respect to the water, it moves along with the earth from west to east with a speed v_e = R . The equation of motion for the pendulum bob in the inertial frame (center of the earth) is: mg - T₀ = m v_e^2 R = m ^2 R T₀ = mg - m ^2 R When the ship sails from east to west at a speed v , its net absolute speed in the inertial frame becomes v' = R - v . The new equation of motion is

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