Solved: PHYSICS Question for NEET

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A particle is displaced through $(3\hat i+4\hat j)\text{ m}$ by force $2\hat i\text{ N}$ . The work done is:

14 J

8 J

6 J

10 J

Identify the Formula: Work done ( $W$ ) by a constant force is defined as the scalar (dot) product of the force vector ( $\mathbf{F}$ ) and the displacement vector ( $\mathbf{d}$ ). $W = \mathbf{F} \cdot \mathbf{d}$ [Class 11 Physics, Ch 6, Sec 6.3, Eq 6.4]
Identify Given Values: $\mathbf{F} = 2\hat i\text{ N}$ $\mathbf{d} = (3\hat i + 4\hat j)\text{ m}$
Calculate Dot Product: Using the property of scalar products of unit vectors where $\hat i \cdot \hat i = 1$ and $\hat i \cdot \hat j = 0$ [Class 11 Physics, Ch 6, Sec 6.1.1, Eq 5.1c]: $W = (2\hat i) \cdot (3\hat i + 4\hat j)$ $W = (2)(3)(\hat i \cdot \hat i) + (2)(4)(\hat i \cdot \hat j)$ $W = 6(1) + 8(0) = 6\text{ J}$

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