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is a perfect square. a) 91 b) 99 c) 1...

______ is a perfect square.
a) 91
b) 99
c) 121
d) 44

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`M=4/3piR^3rho`
`M^1=4/3pix_1^3rho`
`M^1=(M/R^3)pi_1^3`
a. F=GravitatioN/A force
Exerted by the earth on the particle of mass m is
`F=(GM_1m)/x_1^2=(GMm)/R^3x_1^3/x_1^2`
`=(GMm)/R^3 x_1=((GMm)/R^3)/([x^2+(R^2/4)])`
`F_y=Fcostheta`
`=(GMmx_1)/R^3 x/x_1=(GMmx)/R^2`
`F_x=Fsintheta`
`=(GMmx_10/R^3 R/(2x_1)=(GMm)/(2R^2)`
`F-x=(GMm)/R^2`
[since normal force exerted by the wall N=Fx]
Resultant force =`(GMmx)/R^3`
Acceleration=Driving force/mass
`=(GMmx)/(R^3m)=(GMx)/R^3`
So a alphax (the body makes SHM).
`:.a/x=w^2=(GM)/R^3`
`rarr v=sqrt((GM)/R^3)`
`rarr T=2pi(R^3/(GM))`
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