SATHEE: Kinematics 6 Question 7

Kinematics 6 Question 7

7. In the arrangement shown in the figure, the ends $P$ and $Q$ of an unstretchable string move downwards with uniform speed $U$ . Pulleys $A$ and $B$ are fixed. Mass $M$ moves upwards with a speed

(1982, 3M)

(a) $2 U \cos θ$

(b) $\frac{U}{\cos θ}$

(d) $U \cos θ$

Show Answer

Answer:

Correct Answer: 7. (b)

Solution:

In the right angle $△ P Q R$

$l^{2} = c^{2} + y^{2}$

$C =$ constant, $/$ and $y$ are variable

Differentiating this equation with respect to time, we get

$2 l \frac{d l}{d t} = 0 + 2 y \frac{d y}{d t}$ or $- \frac{d y}{d t} = \frac{l}{y} - \frac{d l}{d t}$

Here, $- \frac{d y}{d t} = v_{M}$

$\Rightarrow \frac{l}{y} = \frac{1}{\cos θ}$ and $- d l / d t = U$

Hence,

$v_{M} = \frac{U}{\cos θ}$

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Kinematics 6 Question 7

7. In the arrangement shown in the figure, the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed

Answer:

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7. In the arrangement shown in the figure, the ends $P$ and $Q$ of an unstretchable string move downwards with uniform speed $U$ . Pulleys $A$ and $B$ are fixed. Mass $M$ moves upwards with a speed