Spotlight S rotates in a horizontal plane with a constant angular velocity of 0.1rads- 1 . The spot of light P moves along the wall at a distance of 3m . The velocity of the spot P when θ =45° (see. fig.) is

Question

Spotlight S rotates in a horizontal plane with a constant angular velocity of 0.1rads- 1 . The spot of light P moves along the wall at a distance of 3m . The velocity of the spot P when θ =45° (see. fig.) is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-fmyvwetfcmwckkmq.jpg" /> (A) 0.6 m s- 1 (B) 0.2ms- 1 (C) 0.3 m s- 1 (D) 0.1ms- 1

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-fmyvwetfcmwcytfn.jpg" /> texttan θ = ( textSM/ textPM) ∴ textPM=( textSM/ texttan θ )=3cotθ v=3|cosec2 θ |(d θ /d t) For θ =45° v=rÏ=3× 2× 0.1=0.6 m s- 1

Q. Spotlight $S$ rotates in a horizontal plane with a constant angular velocity of $0.1 r a d s^{- 1}$ . The spot of light $P$ moves along the wall at a distance of $3 m$ . The velocity of the spot $P$ when $θ = 4 5^{\circ}$ (see. fig.) is

$0.6 m s^{- 1}$

$0.2 m s^{- 1}$

$0.3 m s^{- 1}$

$0.1 m s^{- 1}$

$tan θ = \frac{SM}{PM}$
$∴ PM = \frac{SM}{tan θ} = 3 co tθ$ $v = 3 ∣ ∣ cose c^{2} θ ∣ ∣ \frac{d θ}{d t}$ For $θ = 4 5^{\circ}$ $v = r ω = 3 \times 2 \times 0.1 = 0.6 m s^{- 1}$

Q. Spotlight S rotates in a horizontal plane with a constant angular velocity of 0.1rads−1 . The spot of light P moves along the wall at a distance of 3m . The velocity of the spot P when θ=45∘ (see. fig.) is

0.6ms−1

0.2ms−1

0.3ms−1

0.1ms−1