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Standard XII

Physics

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A force exert...

Question

A force exerts an impulse $I$ on a particle changing its speed from $u$ to $2 u$ . The applied force and the initial velocity are oppositely directed along the same line. The work done by the force is:

\frac{3}{2} I u

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\frac{1}{2} I u

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I u

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2 I u

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Solution

The correct option is B $\frac{1}{2} I u$
Impulse, $I =$ change of momentum $= 2 m u - (- m u) = 3 m u$
Work done, $W =$ change of kinetic energy $= \frac{1}{2} m (2 u)^{2} - \frac{1}{2} m u^{2} = \frac{3}{2} m u^{2} = \frac{1}{2} I u$

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A force exerts an impulse I on a particle changing its speed from u to 2u. The applied force and the initial velocity are oppositely directed along the same line. The work done by the force is:

The correct option is B 12IuImpulse, I=change of momentum=2mu−(−mu)=3muWork done, W= change of kinetic energy=12m(2u)2−12mu2=32mu2=12Iu

A force exerts an impulse $I$ on a particle changing its speed from $u$ to $2 u$ . The applied force and the initial velocity are oppositely directed along the same line. The work done by the force is:

The correct option is B $\frac{1}{2} I u$
Impulse, $I =$ change of momentum $= 2 m u - (- m u) = 3 m u$
Work done, $W =$ change of kinetic energy $= \frac{1}{2} m (2 u)^{2} - \frac{1}{2} m u^{2} = \frac{3}{2} m u^{2} = \frac{1}{2} I u$