Q.A particle moves from rest at A on the surface of a smooth cylinder of radius r as shown.At B it leaves the cylinder.The equation relating alpha and beta is a.)3sin(alpha)=2cos(beta) b.)2sin(alpha)=3cos(beta) c.) 3sin(beta)=2cos(alpha) d.)2sin(beta)=3cos(alpha)

Raj Deol Grade: 11

        

Q.A particle moves from rest at A on the surface of a smooth cylinder of radius r as shown.At B it leaves the cylinder.The equation relating alpha and beta is

a.)3sin(alpha)=2cos(beta)

b.)2sin(alpha)=3cos(beta)

c.) 3sin(beta)=2cos(alpha)

d.)2sin(beta)=3cos(alpha)

7 years ago

Answers : (1)

vikas askiitian expert

510 Points

										let the horizonta lsurface of sphere is at zero potential....radius of sphere os R...
at point A ,
     KE is 0 ,PE =mgRcos(alpha)
at point B
 KE=mv² /2 , PE=mgRsin(beta)
applying conservation of energy
 total energy initial = total energy final
 mv² /2 = mgR{cos(alpha)- sin(beta)}................1
on resolving weight in two components will give one in direction opposite to normal reaction at point B...
so we can say that centripital force is provided by wsin(beta) only because normal reaction is 0 at this point as the body loses contact....
        wsin(beta)=mgsin(beta)=mv² /R...............2
 on solving 1 and 2 we get
     3sin(beta)=2cos(alpha)
hence option c is correct....