1) Two spheres are cut from a certain uniform rock. One has radius 4.50 cm. The...

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Question

1) Two spheres are cut from a certain uniform rock. One has radius 4.50 cm. The mass of the other is five times greater. Find its radius.

Answer 1

Answer #1

Density will be same for bot.

Equating the densities:

rho1 = rho2

=> m1/V1 = m2/V2

=> m1/[(4/3)*Pi*r1^3] = m2/ [(4/3)*Pi*r2^3]

But it is given that m2 = 5m1.

Therefore:

m1/[(4/3)*Pi*r1^3] = 5m1/ [(4/3)*Pi*r2^3]

=> 1/r1^3 = 5 / r2^3

=> r2^3 = 5*r1^3

=> r2^3 = 5*(4.5^3)

=> r2^3 = 455.625

=> r2 = 7.69 cm

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Answer 2

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