Conservation of Mechanical Energy — JEE Main Physics MCQs with Solutions
Free JEE Main Physics Conservation of Mechanical Energy MCQs with step-by-step solutions (8 questions). Part of Work, Power and Energy. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Conservation of Mechanical Energy · easy · theory
A mass oscillating on a spring (no friction) has its maximum kinetic energy:
A. At the mean (equilibrium) position ✓ Correct
B. The KE is constant
C. At the extreme positions
D. Halfway to the extreme
Solution: KE + ½kx² = constant; KE is largest where the spring PE is least — at x = 0 (the mean position).
Q2 — Conservation of Mechanical Energy · medium · theory
A roller-coaster car climbs a hill with the motor OFF (smooth track). As it rises, its:
A. Total mechanical energy decreases
B. Speed decreases as KE converts to PE ✓ Correct
C. PE decreases
D. Speed stays constant
Solution: With no engine or friction, ½mv² + mgh = constant, so rising (h↑) costs speed (v↓).
Q3 — Conservation of Mechanical Energy · easy · numerical
A 2 kg block moving at 10 m/s on a smooth floor hits a spring of k = 800 N/m. The maximum compression of the spring is:
A. 0.25 m
B. 1 m
C. 0.5 m ✓ Correct
D. 2 m
Solution: ½mv² = ½kx² ⇒ x = v√(m/k) = 10√(2/800) = 10×0.05 = 0.5 m.
Q4 — Conservation of Mechanical Energy · medium · numerical
A 0.5 kg ball is projected vertically up with 40 J of kinetic energy. The maximum height reached is:
A. 80 m
B. 16 m
C. 8 m ✓ Correct
D. 4 m
Solution: KE → PE: h = KE/mg = 40/(0.5×10) = 8 m.
Q5 — Conservation of Mechanical Energy · hard · numerical
A 1 kg bob on a string is released from the horizontal position. At the lowest point of the swing, the tension in the string is:
A. 30 N ✓ Correct
B. 20 N
C. 10 N
D. 40 N
Solution: v² = 2gL at the bottom; T − mg = mv²/L = 2mg ⇒ T = 3mg = 30 N. Trap: T ≠ mg — the bob is accelerating centripetally.
Q6 — Conservation of Mechanical Energy · medium · numerical
A projectile is fired at 20 m/s. At the top of its path its speed is 12 m/s (the horizontal component). The maximum height reached is:
A. 20 m
B. 7.2 m
C. 16 m
D. 12.8 m ✓ Correct
Solution: Energy per kg: h = (u² − v_top²)/2g = (400 − 144)/20 = 12.8 m.
Q7 — Conservation of Mechanical Energy · hard · numerical
A ball on a string just completes a vertical circle of radius 2.5 m. Its minimum speed at the topmost point is:
A. 10 m/s
B. 2.5 m/s
C. 5 m/s ✓ Correct
D. 7.1 m/s
Solution: At the top for the critical case: mg = mv²/r ⇒ v = √(gr) = √25 = 5 m/s.
Q8 — Conservation of Mechanical Energy · medium · numerical
A spring gun has k = 900 N/m compressed by 0.2 m. It fires a 1 kg ball horizontally. The launch speed is:
A. 6 m/s ✓ Correct
B. 18 m/s
C. 9 m/s
D. 3 m/s
Solution: ½kx² = ½mv² ⇒ v = x√(k/m) = 0.2×30 = 6 m/s.