Find the Compression -2!

Classical Mechanics Level 4

A cubical block of volume V V and density 3 ρ 3\rho is placed inside a liquid of density ρ \rho and attached to a spring of spring constant k k as shown in the figure. Assuming ideal spring and pulley and spring is attached at A A which is at R 2 \frac{R}{2} from center. The compression in the spring at equilibrium is:

4 ρ V g k \frac{4\rho Vg}{k} 2 ρ V g k \frac{2\rho Vg}{k} ρ V g k \frac{\rho Vg}{k} None of these choices 3 ρ V g k \frac{3\rho Vg}{k}

Nishant Rai by Nishant Rai , 25, India

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1 solution

Tanishq Varshney
May 24, 2015

Let T be the tension . Let B be the buoyant force.

balancing forces

T + B = m g T+B=mg

T = 2 ρ V g T=2 \rho Vg

balancing torque

T R = k x R 2 TR=kx\frac{R}{2}

x = 4 ρ V g k \huge{x=\frac{4 \rho Vg}{k}}

7 Helpful 0 Interesting 0 Brilliant 0 Confused

NiCe problem Bhaiya.

Kushal Patankar - 6 years ago

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