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Q104
(NDA-II/2019)
Science & Technology › Basic Science (Physics, Chemistry, Biology) › Basic mechanics concepts
A rigid of mass 2 kg is dropped from a stationary balloon kept at the height of 50 m from the ground. The speed of the body when it just touches the ground and the body when it just touches the ground and the total energy when it is dropped from the balloon are respectively. (acceleration due to gravity = 9.8 m/s 2)
Result
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Correct:
D
Explanation
To find the speed of the body just before it touches the ground, we use the equation of motion for free fall: v² = u² + 2gh. Given the initial velocity (u) is 0 m/s, the height (h) is 50 m, and acceleration due to gravity (g) is 9.8 m/s², the calculation becomes v² = 0 + 2 × 9.8 × 50, which equals 980. Thus, the final speed (v) is √980 m/s. The total mechanical energy of the body when it is dropped is equal to its initial gravitational potential energy, calculated using the formula E = mgh. Substituting the mass (m = 2 kg), gravity (g = 9.8 m/s²), and height (h = 50 m), the total energy is 2 × 9.8 × 50 = 980 J. Therefore, the speed is √980 m/s and the total energy is 980 J.
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