In a rigid body in plane motion, the point {R} is accelerating with respect to point {P} at 10 \angle 180^{\circ} {m} {/} {s}^{2} . If the instantaneous acceleration of point {Q} is zero, the acceleration (in {m} {/} {s}^{2} ) of point {R} is

Correct Answer is : None of above

GATE Mechanical Engineering (ME) 2018 Shift 2 Solved Paper

Question : 45 of 65

Marks: +1, -0

In a rigid body in plane motion, the point

{R}

is accelerating with respect to point

{P}

10 ∠ 180^{∘} {m} {/} {s}^{2} .

If the instantaneous acceleration of point

{Q}

is zero, the acceleration (in

{m} {/} {s}^{2}

) of point

{R}

Solution:

Since acceleration of point Q is zero, so body PQR is hinged at Q.

\ov{{a}}_{R ρ}=\ov{{a}}_{R}-\ov{{a}}_{p}=10 {m} {/} {s}^{2}<180^{∘}

a_{R P}=(R P) ω^{2}=10

20 ω^{2}=10

ω=\;{1}/{√{2}}

a_{R}=Q R(ω^{2})

=16 × \;{1}/{2}=8 {m} {/} {s}^{2}

So the angle of it from reference is
from

△ P Q R

\tan θ=\;{12}/{16}

⇒ \;\; θ=36.8698^{∘}

So,

180+36.8698=216.8698 ; 217^{∘}

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