A force of $10 \mathrm{~N}$ acting at an angle on a particle produces a displacement of $(3 \hat{i}-4…

A force of $10 \mathrm{~N}$ acting at an angle on a particle produces a displacement of $(3 \hat{i}-4 \hat{\jmath}) \mathrm{m}$. Due to this force, if the kinetic energy of the particle is decreased by 25 joule, then the angle between the force and the displacement is
  1. $\cos ^{-1}\left(\frac{1}{3}\right)$
  2. $30^{\circ}$
  3. $120^{\circ}$
  4. $\cos ^{-1}\left(\frac{3}{4}\right)$

Solution

$\begin{aligned} & \text { Work done }=\overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{r}} \\ & \Rightarrow-25=\text { Fr } \cos \theta \quad[\because \text { Work done }=\Delta \mathrm{K}] \\ & \Rightarrow-25=10 \times 5 \times \cos \theta \\ & \Rightarrow \cos \theta=-1 / 2 \\ & \Rightarrow \theta=120^{\circ}\end{aligned}$

Asked in: AP EAMCET 2022 (06 Jul Shift 1)

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