All three spheres are identical having radius 10 cm. there is no slipping at any point of contact. Plank P and Q are moving in opposite direction with speed 10 and 30 cm/sec. height of instantaneous axis of rotation of sphere A from the gound is

Options

A. 20 cm
B. 30 cm
C. 15 cm
D. 25 cm

Answer

D

Explanation

Let x be the surface distarice of axis of rotation from the top of sphere A (downward). Since angluar velocity of the top and bottom point of sphere A will be same, therefore,
`omega=(30)/(x)=(10)/((2R-x))`
`(30)/(x)=(10)/(20-x)`
`impliesx=15`
`therefore` Distance from ground
`=2R+(2R-x)`
`=20+5=25cm`