Gravitational Field: Practice Problem & Solution
The gravitational field in a region is given by \(vec{I} = 10(\hat{i} + \hat{j})\text{ N/kg}\). The work done by gravitational field to shift a particle of mass \(2\text{ kg}\) from position \((0,0)\) to \((5, 4)\) will be :
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Gravitational Field. Understanding the underlying formula is key to arriving at the correct answer below:
The force is \(\vec{F} = mvec{I} = 2 \times 10(\hat{i} + \hat{j}) = 20\hat{i} + 20\hat{j}\text{ N}\). Displacement is \(\vec{d} = 5\hat{i} + 4\hat{j}\text{ m}\). Work done \(W = \vec{F} \cdot \vec{d} = (20)(5) + (20)(4) = 180\text{ J}\).
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