In a direct impact- loss in kinetic energy is given by K - M1M2-2M1 - M2-V1 - V22 1 - K2 with usualnotationsexcept k- The quality k will have dimensional formula-

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Dimensional Analysis

In a direct i...

Question

In a direct impact, loss in kinetic energy is given by $△ K = \frac{M_{1} M_{2}}{2 (M_{1} + M_{2})} . (V_{1} - V_{2})^{2} (1 - K^{2})$ with usual

notations(except k). The quality k will have dimensional formula:

$[M^{0} L^{2} T^{- 2}]$

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$[M L T^{- 1}]$

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$[M^{0} L^{0} T^{0}]$

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$[M^{0} L T^{- 1}]$

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Solution

The correct option is C
$[M^{0} L^{0} T^{0}]$

Since 1 and $k^{2}$ are being subtracted , they should have the same dimensions. 1 is a number i.e. dimensionless

$[1 - k^{2}] = M^{0} L^{0} T^{0}$

Hence, $[k] = M^{0} L^{0} T^{0}$

Actually, k is the coefficient of restitution.

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Similar questions

In a direct impact, loss in kinetic energy is given by $△ K = \frac{M_{1} M_{2}}{2 (M_{1} + M_{2})} . (V_{1} - V_{2})^{2} (1 - K^{2})$ with usual

notations(except k). The quality k will have dimensional formula:

In a direct impact, loss in kinetic energy is given by
$Δ K = \frac{M_{1} M_{2}}{2 (M_{1} + M_{2})} . (V_{1} - V_{2})^{2} (1 - k^{2})$
with usual notations (except k). The quantity k will have dimensional formula:

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In a direct impact, loss in kinetic energy is given by △K=M1M22(M1+M2).(V1−V2)2(1−K2) with usual notations(except k). The quality k will have dimensional formula:

The correct option is C [M0L0T0] Since 1 and k2 are being subtracted , they should have the same dimensions. 1 is a number i.e. dimensionless [1−k2]=M0L0T0 Hence, [k]=M0L0T0 Actually, k is the coefficient of restitution.

In a direct impact, loss in kinetic energy is given by $△ K = \frac{M_{1} M_{2}}{2 (M_{1} + M_{2})} . (V_{1} - V_{2})^{2} (1 - K^{2})$ with usual

notations(except k). The quality k will have dimensional formula:

The correct option is C
$[M^{0} L^{0} T^{0}]$

Since 1 and $k^{2}$ are being subtracted , they should have the same dimensions. 1 is a number i.e. dimensionless

$[1 - k^{2}] = M^{0} L^{0} T^{0}$

Hence, $[k] = M^{0} L^{0} T^{0}$

Actually, k is the coefficient of restitution.