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Question

A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hands of a person standing in the car. The car is moving with constant acceleration a directed horizontally as shown in figure. The other end of the string is pulled with constant acceleration a vertically. The tension in the string is equal is

  1. mg2+a2
  2. mg2+a2ma
  3. mg2+a2+ma
  4. m(g+a)


Solution

The correct option is C mg2+a2+ma
Free body diagram of the bob can be shown as


As this frame is non-inertial, so to apply Newton's laws of motion we will consider a pseudo force in opposite direction of the acceleration of the frame. 
By using force balance on the bob, the net force on the bob comes out to be
ma=Tmg2+a2
∴    T=ma+mg2+a2

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