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NEET PHYSICSEasy

The minimum work done in pulling up a block of wood weighing 2 kN2 \text{ kN} for a length of 10 m10 \text{ m} on a smooth plane inclined at an angle of 1515^\circ with the horizontal is (given sin15=0.2588\sin 15^\circ = 0.2588):

A

4.36 kJ4.36 \text{ kJ}

B

5.17 kJ5.17 \text{ kJ}

C

8.91 kJ8.91 \text{ kJ}

D

9.82 kJ9.82 \text{ kJ}

Step-by-Step Solution

The minimum force required to pull the block up a smooth inclined plane is equal to the component of its weight along the incline, F=mgsinθF = mg \sin \theta . Given: Weight W=mg=2 kN=2000 NW = mg = 2 \text{ kN} = 2000 \text{ N}, length of incline d=10 md = 10 \text{ m}, and θ=15\theta = 15^\circ. The required force is F=2000×sin15=2000×0.2588=517.6 NF = 2000 \times \sin 15^\circ = 2000 \times 0.2588 = 517.6 \text{ N}. The minimum work done is given by W=F×dW = F \times d . W=517.6 N×10 m=5176 J=5.176 kJ5.17 kJW = 517.6 \text{ N} \times 10 \text{ m} = 5176 \text{ J} = 5.176 \text{ kJ} \approx 5.17 \text{ kJ}. Alternatively, work done equals the change in potential energy =mgh=mg(dsinθ)=2000×10×0.2588=5176 J=5.176 kJ= mgh = mg(d \sin \theta) = 2000 \times 10 \times 0.2588 = 5176 \text{ J} = 5.176 \text{ kJ}.

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