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Question
A man of mass 50 kg starts moving on the earth and acquires a speed 1.8 m/s. With what speed does the earth recoil? Mass of earth = 6 × 1024 kg.
Solution
By the law of conservation of linear momentum, we have:
\[m_1 v_1 = m_2 v_2\]
Here, m1 and v1 are the mass and velocity of the man respectively, and m2 and v2 are the mass and velocity of the Earth respectively.
\[\Rightarrow 50 \times 1 . 8 = 6 \times {10}^{24} \times v_2 \]
\[ \therefore v_2 = \frac{50 \times 1 . 8}{6 \times {10}^{24}} = 15 \times {10}^{- 24} m/s\]
\[ \Rightarrow v_2 = 1 . 5 \times {10}^{- 23} m/s\]
Hence, the earth recoils with a speed of 1.5 × 10−23 m/s.
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