Question
In the system of pulleys shown in figure, P1 is fixed and while P2 is capable of moving freely in vertical direction. Both the pulleys are frictionless and massless. Find the acceleration of m1 and m2 and tensions T1 and T2.
Solution
Let 'a1' and 'a2' be the accelerations of mass m1 in downward direction and mass m2 in upward direction respectively.
Since the displacement of mass m1 is twice that of pulley P2 and hence mass m2, thus the acceleration a1 is equal to twice of acceleration a2.
Hence,
...(1)
Equation of motion of mass
is,
...(2)
Equation of motion of mass
is,
...(3)
Also,
...(4)
Solving the equations, we get
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Now, substituting the values of mass m1 and m2
we get
Acceleration of masses,
and
Tension in the string,
Since the displacement of mass m1 is twice that of pulley P2 and hence mass m2, thus the acceleration a1 is equal to twice of acceleration a2.
Hence,
...(1) Equation of motion of mass
is, ...(2) Equation of motion of mass
is, ...(3) Also,
...(4) Solving the equations, we get
and
Now, substituting the values of mass m1 and m2
we get
Acceleration of masses,
and
Tension in the string,
