A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point A is 10 ~m / s . The ratio of its kinetic energies at point B and C is : (Take acceleration due to gravity as 10 ~m / s ^2 )

Step-by-step solution

aligned & 1 2 ~m 100+0= 1 2 mV _ B ^2+ mg ( R - R 3 2 ) & 100= V _ B ^2+2 gR (1- 3 2 ] & V _ B ^2=100-20(2- 3 ) & . V _ B ^2=60+20 3 ) & K . E _ B = 1 2 mV _ B ^2= m 2 (60+20 3 ) & 1 2 ~m (100)= 1 2 mV & 2 & 100= mg ( 3 R 2 ) & 100 ~V _ C ^2=60 & ~V _ C ^2=40 & ~K . E _ C = 1 2 mV V _ C ^2= 1 2 ~m (40) & K . E _ B = 60+20 3 40 = 3 2 + 3 2 = 3+ 3 2 aligned