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
- AT₀ + m v
- BT₀ + 2 m v
- CT₀ - m v
- 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