Two objects of unequal mass are connected by a massless cord passing over a frictionless pulley. After the objects are released from rest, which of the following statements is true? (U = gravitational potential energy, K = kinetic energy of the system.)

a) ∆U < 0 and ∆K > 0
b) ∆U = 0 and ∆K > 0
c) ∆U < 0 and ∆K = 0
d) ∆U = 0 and ∆K = 0
e) ∆U > 0 and ∆K <0

a) ∆U < 0 and ∆K > 0

Explanation:

The initial kinetic energy is zero since the objects are at rest

KE₁ = 0

The final kinetic energy is positive which means

KE₂ > 0

Therefore, the change is kinetic energy is positive

∆KE > 0

The change in gravitational potential energy is negative since the masses are unequal

Lets suppose mass of 1st object is m₁ and mass of 2nd m₂ and  m₂ > m₁

∆U = m₁gh (positive)

∆U = m₂gh (negative)

Since m₂ > m₁ Total change in gravitational potential energy will be negative

∆U < 0

Therefore, the correct option is (a)

∆U < 0 and ∆K > 0

Check attachment for solution

Explanation:

(75°f − 32) × 5/9 = 23.889°c