A leak-proof cylinder of length 1 ; m, made o | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $A$ be the cross-sectional area of the cylinder and $\rho_0$ and $\rho_4$ be the densities of water at $0^{\circ} C$ and $4^{\circ} C$ respect

Vedclass · Accepted Answer

$1.01$

Vedclass · Answer

(A) Let $A$ be the cross-sectional area of the cylinder and $ho_0$ and $ho_4$ be the densities of water at $0^{\circ} C$ and $4^{\circ} C$ respectively.At $0^{\circ} C,$ the submerged length of the cylinder is $h_0 = 100 \; cm - 20 \; cm = 80 \; cm.$By the principle of flotation,the weight of the cylinder equals the weight of the displaced water:$mg = A 	imes h_0 	imes ho_0 	imes g \implies m = A 	imes 80 	imes ho_0.$At $4^{\circ} C,$ the submerged length of the cylinder is $h_4 = 100 \; cm - 21 \; cm = 79 \; cm.$Since the mass of the cylinder remains constant:$m = A 	imes 79 	imes ho_4.$Equating the two expressions for $m$:$A 	imes 80 	imes ho_0 = A 	imes 79 	imes ho_4.$Therefore,the ratio of the density at $4^{\circ} C$ to the density at $0^{\circ} C$ is:$\frac{ho_4}{ho_0} = \frac{80}{79} \approx 1.0126.$Rounding to the nearest given option,the value is close to $1.01$.

Similar Questions

At what depth does a body remain in equilibrium in a liquid? Explain.

$A$ cork is submerged in water by a spring attached to the bottom of a pail. When the pail is kept in an elevator moving with an acceleration downwards,the spring length

$A$ solid sphere of density $\rho_s$ which is $\eta$ $( > 1)$ times lighter than water (density $\rho_w$) is suspended in a water tank by a string tied to its base as shown in the figure. If the mass of the sphere is $m$,then the tension in the string is given by:

If $W$ is the weight of a body of density $\rho$ in vacuum,then its apparent weight in air of density $\sigma$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module