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ago in Physics by (12.7k points)

A ball of mass 0.5 kg is dropped from a height of 40 m. The ball hits the ground and rises to a height of 10 m. The impulse imparted to the ball during its collision with the ground is (Take \(g = 9.8 \ m/s^2\))

(1) 21 NS

(2) 7 NS

(3) 0

(4) 84 NS

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1 Answer

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ago by (15.4k points)

Correct option is : (1) 21 NS

. A ball of mass 0.5 kg

\( v_{1}=\sqrt{2 g h_{1}}\)

\( =\sqrt{2 \times 9.8 \times 40}\)

\( v_{1}=\sqrt{784}=28 \mathrm{~m} \mathrm{~s}^{-1}\)

\(v_{2}=\sqrt{2 g h_{2}}=\sqrt{2 \times 9.8 \times 10}\)

\( =\sqrt{196}=14 \mathrm{~m} \mathrm{~s}^{-1}\)

\( \text{Impulse}\ =\Delta \vec{p}=m\left(\vec{v}_{f}-\vec{v}_{i}\right)=m\left(\vec{v}_{2}-\vec{v}_{1}\right)\)

\(\frac{1}{2}(14-(-28))\)

\( =21 \ NS\)

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