KVPY2017PhysicsRotational Motion
One end of a rod of length L=1 ~m is fixed to a point on the circumference of a wheel of radius R =1 / 3 ~m . The other end is sliding freely along a straight channel passing through the center O of the wheel as shown in the figure below. The wheel is rotating with a constant angular velocity about O .
Options
- A2 3
- B3
- C2 3
- D3
Correct answer
A. 2 3
Step-by-step solution
60^ = L R = 1 1 / 3 = 3 = x = 1+ 1 3 = 2 3 = R ²+ x ²- L ² 2 Rx R ²+ x ²- L ²=2 Rx aligned 2 x dx dt =2 R [ x (- )+ dx dt ] & dx dt [ x - R ]=- Rx d dt -& dx dt = v & d dt = aligned v = R x x - R aligned &= 1 3 2 3 3 2 2 3 - 1 3 1 2 = 3 1 3 3 2 = 2 3 v =& 2 3 aligned