Three point particles P, Q, R move in a circle of radius 'r' with different but constant speeds. They start
moving at t = 0 from their initial positions as shown in the figure. The angular velocities (in rad/sec) of P,Q and R are 5pi, 2pi & 3pi respectively, in the same sense. The time interval after which they all meet is:-
(1) 2/3 sec
(2) 1/6 sec
(3) 1/2 sec
(4) 3/2 sec
pls explain with correct explanation and answer...
(irrelevants and incorrect will get report)
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Angular velocity of P, = 5π rad/s
Angular velocity of Q, = 2π rad/s
Angular velocity of R, = 3π rad/s
Now, let's assume P as the origin. So,
• Angle travelled by P, θ = × t = 5πt - (i)
• Angle travelled by Q, θ = × t = 2πt - (ii)
• Angle travelled by R, θ = × t = 3πt - (iii)
Let's use the rule of elimination, in equation (i), (ii) and (iii). So,
• 5πt = 5π × =
• 2πt = 2π × + =
• 3πt = 3π × + π = 2π
Similarly, when t was either or , the value of θ was different. The value of θ should be between 0 and 2π. Now, we put the value of t = . Now,
• 5πt = 5π × = - (a)
• 2πt = 2π × + = - (b)
• 3πt = 3π × + π = - (c)
But the value of θ is different in the above equations. As we know,
• = 6π +
• = 2π +
• = 4π +
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