A rectangular block of mass m and area of cro | vedclass

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

Question

(C) Let $l$ be the length of the block immersed in the liquid at equilibrium. When the block is floating,the weight of the block is balanced by the bu

Vedclass · Accepted Answer

$T \propto \frac{1}{\sqrt{A}}$

Vedclass · Answer

(C) Let $l$ be the length of the block immersed in the liquid at equilibrium. When the block is floating,the weight of the block is balanced by the buoyant force:$mg = A l \rho g$If the block is given a small vertical displacement $y$ downwards,the additional buoyant force acting upwards is:$F_{restoring} = -(A(l+y)\rho g - mg) = -(Al\rho g + Ay\rho g - mg)$Since $mg = Al\rho g$,we get:$F_{restoring} = -A\rho g y$This is the equation of simple harmonic motion $F = -ky$,where the spring constant $k = A\rho g$.The time period $T$ of the oscillation is given by:$T = 2\pi \sqrt{\frac{m}{k}} = 2\pi \sqrt{\frac{m}{A\rho g}}$From this expression,we can see that $T \propto \frac{1}{\sqrt{A}}$.

$A$ rectangular block of mass $m$ and area of cross-section $A$ floats in a liquid of density $\rho$. If it is given a small vertical displacement from equilibrium,it undergoes simple harmonic motion with a time period $T$. Then:

Similar Questions

$A$ particle of mass $5 \times 10^{-5} \ kg$ is placed at the lowest point of a smooth parabola $x^2 = 40y$ ($x$ and $y$ in $m$). If it is displaced slightly such that it is constrained to move along the parabola,the angular frequency of oscillation (in $rad/s$) will be approximately:

$A$ $U$-tube of uniform bore of cross-sectional area $A$ has been set up vertically with open ends facing up. Now $M$ grams of a liquid of density $d$ is poured into it. The column of liquid in this tube will oscillate with a period $T$ such that

$A$ rectangular block of mass '$m$' and cross-sectional area '$A$' floats on a liquid of density '$\rho$'. It is given a small vertical displacement from equilibrium, it starts oscillating with frequency ($g$ = acceleration due to gravity).

Vedclass Test Series

Exam Paper Generator

Online Exam Module