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Question

In the given figure find the velocity of the block $$M$$, if both the rope ends are pulled with a velocity $$v$$.
133589_19afe38a43154979a84a24b4745cdbe6.png


A
2vcosθ
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B
vcosθ
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C
v2cosθ
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D
2vcosθ
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Solution

The correct option is B $$\displaystyle \frac {v}{\cos \theta}$$
$$l^{2}=x^{2}+y^{2}$$
Differentiating with respect to t,
$$2l \displaystyle \frac{dl}{dt}=0 + 2y \displaystyle \frac{dy}{dt}$$ ($$\because x$$ is constant its derivative is zero)
$$\displaystyle \frac{dy}{dt}=\displaystyle \frac{dl/dt}{y/l}=\displaystyle \frac{v}{\cos \theta }$$ 
129829_133589_ans_39a7d68b109f41ee94d273f510ab7f51.png

Physics

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