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Let Vs be the volume of sphere, Vc be the volume of cavity, and Vt be the total volume, ie. Vt=Vc + Vs.After drawing the FBD, We get Fb - mg = ma (Fb - force of buoyancy)Thus, d1Vtg – d2Vsg = d2VsaPut Vt = Vs+Vcd1(Vs + Vc)g – d2Vsg = d2Vsa.d1(Vs + Vc)g = d2Vs(a+g)d1Vsg+ d1Vcg =d2Vs(a+g)d1Vcg = d2Vs(a+g) – d1Vsgd1Vcg = d2Vs[(a+g) – d1/d2g]d2Vs = mTherefore, d1Vcg = m[(a+g) – d1/d2g]Hence, Vc = {m[(a+g) – d1/d2g]} / d1gOn further simplifying, you’ll get the answer, according to the options given...m[(a+g)−d1/d2]d1gm[(a+g)−d1/d2]d1
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