Two identical sleeves A and B each of mass m can slide without friction on a fixed horizontal rod. A load C of mass 2m is suspended from the mid-point of a light inextensible cord of length l=33 m connecting the sleeves A and B. Initially the sleeves are at a separation l and the load is held motionless. What can you conclude for subsequent motion after the load is released? Acceleration of free fall is 10 m/s2.

BCDFrom constraintϑcosθ=ϑ0sinθ …………. (1)From energy conservation.mcgl2sinθ=12mϑ2×2+12mcϑ02 ………… (2)From (1) & (2) ϑ0=f(θ)For maximum of ϑ0;dϑdθ=0

Two identical sleeves A and B each of mass m can slide without friction on a fixed horizontal rod. A load C of mass 2m is suspended from the mid-point of a light inextensible cord of length l=33 m connecting the sleeves A and B. Initially the sleeves are at a separation l and the load is held motionless. What can you conclude for subsequent motion after the load is released? Acceleration of free fall is 10 m/s2.

BCDFrom constraintϑcosθ=ϑ0sinθ …………. (1)From energy conservation.mcgl2sinθ=12mϑ2×2+12mcϑ02 ………… (2)From (1) & (2) ϑ0=f(θ)For maximum of ϑ0;dϑdθ=0

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Two identical sleeves A and B each of mass m can slide without friction on a fixed horizontal rod. A load C of mass 2m is suspended from the mid-point of a light inextensible cord of length $l = 3 \sqrt{3}$ m connecting the sleeves A and B. Initially the sleeves are at a separation $l$ and the load is held motionless. What can you conclude for subsequent motion after the load is released? Acceleration of free fall is ${10 m/s}^{2}$ .

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The load descends a height 1.5 m to acquire maximum speed.

Maximum speed acquired by the load C is $2 \sqrt{5} m/s.$

Before the sleeves collide, the net force on the system consisting of the sleeves, the cord and the load becomes zero once.

Maximum speed of the sleeves is $\sqrt{10} m/s.$

answer is B, C, D.

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Detailed Solution

BCD
Question Image
From constraint
$ϑ \cos θ = ϑ_{0} \sin θ$ …………. (1)
From energy conservation.
$m_{c} g \frac{l}{2} \sin θ = \frac{1}{2} m ϑ^{2} \times 2 + \frac{1}{2} m_{c} ϑ_{0}^{2}$ ………… (2)
From (1) & (2) $ϑ_{0} = f (θ)$
For maximum of $ϑ_{0}; \frac{d ϑ}{d θ} = 0$