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The following item consists of two statements, one labelled the Assertion (A) and the other labelled the Reason (R). You are to examine these two statements carefully and decide if the Assertion (A) and Reason (R) are individually true and if so, whether the reason is a correct explanation of the Assertion. Select your answer using the codes given below. Assertion (A) : The work done when the force and displacement are perpendicular to each other is zero.
Reason (R) : the dot product $\vec{A} \cdot \vec{B}$ vanishes, if the vector
$\vec{A}$ and $\vec{B}$ are perpendicular.
Options:
Reason (R) : the dot product $\vec{A} \cdot \vec{B}$ vanishes, if the vector
$\vec{A}$ and $\vec{B}$ are perpendicular.
Solution:
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Verified Answer
The correct answer is:
Both A and $\mathrm{R}$ are true but $\mathrm{R}$ is not the correct explanation of A
(A) We know that
Work done $=\overrightarrow{\mathbf{F}} \cdot \overrightarrow{\mathbf{d}}=|\overrightarrow{\mathbf{F}}| \cdot|\overrightarrow{\mathbf{d}}| \cos \theta$
Since, $\theta=90^{\circ}$
$\Rightarrow$ work done $=|\overrightarrow{\mathbf{F}}| \cdot|\overrightarrow{\mathbf{d}}| \cos 90^{\circ}=0$
(R) $\overrightarrow{\mathbf{A}} \cdot \overrightarrow{\mathbf{B}}=0$
$\Rightarrow \overrightarrow{\mathbf{A}}$ and $\overrightarrow{\mathbf{B}}$ are perpendicular. Both $\mathrm{A}$ and $\mathrm{R}$ are true but $\mathrm{R}$ is not correct explanation of
A.
Work done $=\overrightarrow{\mathbf{F}} \cdot \overrightarrow{\mathbf{d}}=|\overrightarrow{\mathbf{F}}| \cdot|\overrightarrow{\mathbf{d}}| \cos \theta$
Since, $\theta=90^{\circ}$
$\Rightarrow$ work done $=|\overrightarrow{\mathbf{F}}| \cdot|\overrightarrow{\mathbf{d}}| \cos 90^{\circ}=0$
(R) $\overrightarrow{\mathbf{A}} \cdot \overrightarrow{\mathbf{B}}=0$
$\Rightarrow \overrightarrow{\mathbf{A}}$ and $\overrightarrow{\mathbf{B}}$ are perpendicular. Both $\mathrm{A}$ and $\mathrm{R}$ are true but $\mathrm{R}$ is not correct explanation of
A.
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