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What will be the time period of the pendulum of length l suspended from the ceiling of a cart which is sliding without friction on an inclined plane of inclination θ ?

Options

  1. A2 π l ⁡ g cos θ
  2. B2 π 3 l ⁡ g cos θ
  3. C4 π 2 l ⁡ g cos θ
  4. D3 π 4 l ⁡ 2g cos θ

Correct answer

A. 2 π l ⁡ g cos θ

Step-by-step solution

Here, point of suspension has an acceleration. a → = g sin θ (down the plane). Further, g → can be resolved into two components g sin θ (along the plane) and g cos θ (perpendicular to plane). g → eff = g → - a → = g cosθ (perpendicular to plane) T = 2 π l ⁡ | g → eff |   = 2 π l ⁡ g cos θ

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