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Kinetic Energy Formulae

The velocity ...

Question

The velocity ' $V$ ' of a particle varies with distance ' $x$ ' and time ' $t$ ' as $V = A s i n (B x) c o s (C t)$ when $A, B, C$ are constants, then $\frac{A B}{C}$ will have the dimensions of:

velocity

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acceleration

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pressure

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strain

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Solution

The correct option is B strain
$V = A s i n (B x) C o s (C t)$
A has the same dimension as V $\Rightarrow A = L T^{- 1}$
Ct and Bx has the same dimension as $M^{0} L^{0} T^{0}$
i.e it should be dimensionless.
$\Rightarrow B x = M^{0} L^{0} T^{0}$
$B = M^{0} L^{- 1} T^{0}$
$C t = M^{0} L^{0} T^{0}$
$\Rightarrow C = M^{0} L^{0} T^{- 1}$
$S o, \frac{A B}{c} = \frac{(L^{1} T^{- 1}) (M^{0} L^{- 1} T^{0})}{(M^{0} L^{0} T^{- 1})} = M^{0} L^{0} T^{0}$
Out of the above option, only strain is dimensionless.
Hence, option D is correct.

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The velocity 'V' of a particle varies with distance 'x' and time 't' as V=Asin(Bx)cos(Ct) when A,B,C are constants, then ABC will have the dimensions of:

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