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Standard XII

Physics

Race of Rollers

A metal spher...

Question

A metal sphere of mass m having cavity inside has an instantaneous upward acceleration 'a' when released from rest fully submerged in a liquid of density $d_{1}$ . Taking the density of the metal as $d_{2}$ , find the volume of the cavity in the sphere.

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Solution

$n e t f o r c e v d_{1} g - m g$
$a = \frac{v d_{1} g - m g}{m}$
$V = \frac{m a + m g}{d_{1} g}$
V volume of sphere
mass of the metal m is
$= d e n s i t y \times v o l u m e o f m e t a l$
$d 2 (V_{f u l l} - V_{c a v i t y}) = m$
$d 2 (\frac{m a + m g}{d_{1} g} - V_{c a v i t y}) = m$
$V_{c a v i t y} = (\frac{m a + m g}{d_{1} g} - \frac{m}{d_{2}})$

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A metal sphere of mass m having cavity inside has an instantaneous upward acceleration 'a' when released from rest fully submerged in a liquid of density d1. Taking the density of the metal as d2, find the volume of the cavity in the sphere.

netforcevd1g−mga=vd1g−mgmV=ma+mgd1gV volume of sphere mass of the metal m is =density×volumeofmetald2(Vfull−Vcavity)=md2(ma+mgd1g−Vcavity)=mVcavity=(ma+mgd1g−md2)

A metal sphere of mass m having cavity inside has an instantaneous upward acceleration 'a' when released from rest fully submerged in a liquid of density $d_{1}$ . Taking the density of the metal as $d_{2}$ , find the volume of the cavity in the sphere.