A man is moving towards the center of a horizontal circular disk in such a way that he experiences no tangential force acting on him . In doing so he finds that he has a constant radial velocity of 0.5 m / s. He starts his motion when he is at a distance of 10 m from the center and his angular velocity at this instant is 1 rad / s .By how many times has his radial component of force increased when he is 8 m away from the center ?

a ) 2.052
b ) 0.510
c ) 1.947
d ) 1.329

 

Let m be the mass of the man ; w0 and w1 be his angular velocity when he is at a distance of 10 m and 8 m from the center respectively ; a , be his angular acceleration ; R0 and R1 be the radii 10 m and 8 m respectively and Fr 0 and Fr 1 be his radial force when he is at a distance of 10 m and 8 m from the center respectively.

Writing the equation of motion in the tangential direction ,


Substituting the values in the above equation ,
   ( 10 )2( 1 )= ( 8 )2 w1   or   w1 = 1.56 rad / s .

Since ,

The radial component his force at the given radii are ,

Hence the the radial component of his force increased by a factor of 1.947 .