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QJEEM22Phf009: JEE Main 2022 Physics - Class 11 JEEM22Phf009 Solution: The velocity of a small ball of mass 0.3   g and density 8 …

The velocity of a small ball of mass 0.3 g and density 8 g/cc when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 1.3 g/cc, then the value of viscous force acting on the ball will be x×10−4 N, The value of x is _________. [use g=10 m/s2]

Step-by-Step Verified Solution

FV+FB=mg(v=F_{\mathrm{V}}+F_B=m g(v= constant ))

FV=mg−FBF_V=m g-F_B

=ρBVg−ρLVg=\rho_{\mathrm{B}} \mathrm{Vg}-\rho_{\mathrm{L}} \mathrm{Vg}

=(ρB−ρL)Vg=\left(\rho_{\mathrm{B}}-\rho_{\mathrm{L}}\right) \mathrm{Vg}

=(8−1.3)×10+3×0.3×10−38×103×10=(8-1.3) \times 10^{+3} \times \frac{0.3 \times 10^{-3}}{8 \times 10^3} \times 10

=6.7×0.38×10−2( g=10)=\frac{6.7 \times 0.3}{8} \times 10^{-2} \quad(\mathrm{~g}=10)

=67×38×10−4=25.125×10−4=\frac{67 \times 3}{8} \times 10^{-4}=25.125 \times 10^{-4}

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