Explanation:
Power = Work/Time. Work has dimensions [ML²T⁻²], dividing by time [T] gives [ML²T⁻³]. Energy is [ML²T⁻²], force is [MLT⁻²], momentum is [MLT⁻¹]. This dimensional formula uniquely identifies power. Memory tip: Power = energy per second ⇒ dimensions include extra T⁻¹ factor. Frequently tested in dimensional analysis sections of competitive exams.
A body of mass 5 kg is moving with velocity 10 m/s. A constant force acts on it for 2 seconds, changing its velocity to 20 m/s. The magnitude of the force is:
Explanation:
Using Newton's second law: F = ma. First find acceleration: a = (v - u)/t = (20 - 10)/2 = 5 m/s². Then F = 5 kg × 5 m/s² = 25 N. Alternatively, using impulse-momentum theorem: FΔt = mΔv ⇒ F×2 = 5×(20-10) ⇒ F = 50/2 = 25 N. Both approaches confirm. This problem integrates kinematics with dynamics. Exam tip: When time interval is given, impulse-momentum method is often faster. Such questions assess ability to select appropriate physics principles for problem-solving in time-constrained exams.
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