A body of mass 2 kg has momentum 10 kg·m/s. Its kinetic energy is:
A. 100 J
B. 50 J
C. 25 J
D. 12.5 J
Answer: Option D
Solution (By JKExamLibrary)
KE = p²/(2m) = (10)²/(2×2) = 100/4 = 25 J. Wait, recalculate: 100/4 = 25 J. Option B is correct. KE = p²/2m relates momentum and kinetic energy. Memory tip: When given momentum, use KE = p²/2m instead of finding velocity first. Efficient calculation method for competitive exam time constraints.
Two masses, M1 = 3 kg and M2 = 2 kg, are connected by a light inextensible string passing over a frictionless pulley (Atwood machine). The acceleration of the system is (Take g = 10 m/s^2):
Explanation:
For an Atwood machine, the common acceleration of both masses is given by the formula a = [(M1 - M2) / (M1 + M2)] * g. Substituting the given values: a = [(3 - 2) / (3 + 2)] * 10 = (1 / 5) * 10 = 2 m/s^2. The heavier mass accelerates downwards, the lighter one upwards.
Explanation:
Vertical motion is independent of horizontal. t = √(2h/g). Mass doesn't affect. Horizontal velocity affects range, not time of fall. Projectile motion independence of perpendicular components.
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