A small solid sphere of mass M0, of radius R0, and of uniform density p0 is plac

Question

A small solid sphere of mass M0, of radius R0, and of uniform density p0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls, U-Unchanged), when that sphere is replaced by a new solid sphere of uniform density.
Answer choices: R, F, U, R or U, F or U, R or F or U

(a) The new sphere has mass M > M0 and density p = p0

(b) The new sphere has density p< p0 and radius R > R0

(c) The new sphere has radius R = R0 and density p > p0

(d) The new sphere has density p <p0 and mass M = M0

(e) The new sphere has mass M < M0 and density p = p0

(f) The new sphere has density p> p0 and mass M = M0

Explanation / Answer

water level depend only the mass of the sphere if the mass is increased the pressure on the water is also increases then water level rises (a) new sphere mass M>M0 the water level is rises answer:R (b) density is inversily proportional to the volume at same mass from given data density decreases and volume (V =R^3) increases but we canno't say mass is same or less or more answer :R or U or F for same mass :U decreased mass :F increased mass :R (c) in this case volume is same density p >p0 density p =mass/ volume pmass M>M0 there fore answer is :R (d) for same mass answer:U (e) mass M<M0 mass is decreased answer :F
(f) in this case mass is same M=M0 the water level is unchanged answer:U

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