Verified Solution • 2025–26 Session moderate

QAIPMT-2006-Ph-2460: NEET 2006 Physics - Class 11 AIPMT-2006-Ph-2460 Solution: A rectangular block of mass m and area of cross-section 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 with a time period T then

T \propto \frac{1}{\sqrt{m}}

T \propto \sqrt{\rho}

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

T \propto \frac{1}{\sqrt{\rho}}

Multiple Choice Options

A [L], [LT] and [LT $-$ _ 2 ]
B [LT $-$ _ 2 ], [L] and [T]
C [L 2 ], [T] and [LT $-$ _ 2 ]
D [LT $-$ _ 2 ], and [LT] and [L]

Step-by-Step Verified Solution

Given, v = at + b t + c Dimension of at = Dimension of velocity v _ [at] = [LT -1 ] _ [a] = [ L T _ 1 ] [ T ] = [LT -2 ] As c is added to t, _ [c] = [T] [ b ] [ T ] = [LT -1 ] _ [b] = [L]

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