Search any question & find its solution
Question:
Answered & Verified by Expert
A monkey of mass $40 \mathrm{~kg}$ climbs on a rope (fig.) which can stand a maximum tension of $600 \mathrm{~N}$. In which of the following cases will the rope break: the monkey
(a) climbs up with an acceleration of $6 \mathrm{~ms}^{-2}$
(b) climbs down with an acceleration of $4 \mathrm{~ms}^{-2}$
(c) climbs up with a uniform speed of $5 \mathrm{~ms}^{-1}$
(d) falls down the rope nearly freely under gravity? (Ignore the mass of the rope).
(a) climbs up with an acceleration of $6 \mathrm{~ms}^{-2}$
(b) climbs down with an acceleration of $4 \mathrm{~ms}^{-2}$
(c) climbs up with a uniform speed of $5 \mathrm{~ms}^{-1}$
(d) falls down the rope nearly freely under gravity? (Ignore the mass of the rope).
Solution:
1216 Upvotes
Verified Answer
(a) When the monkey climbs up with an acceleration, then
$$
T-m g=m a
$$
where $\mathrm{T}$ represents the tension (figure a).
$$
\begin{array}{ll}
\therefore & T=m g+m a=m(g+a) \\
\text { or } & T=40 \mathrm{~kg}(10+6) \mathrm{ms}^{-2}=640 \mathrm{~N}
\end{array}
$$
But the rope can withstand a maximum tension of 600 N. So the rope will break.
(b) When the monkey is climbing down with an acceleration, then
$$
m g-T=m a \quad \text { (figure (b)) }
$$
$$
\Rightarrow T=m g-m a=m(g-a)
$$
or $\mathrm{T}=40 \mathrm{~kg}(10-4) \mathrm{ms}^{-2}=240 \mathrm{~N}$
The rope will not break.
(c) When the monkey climbs up with uniform speed, then $T=m g=40 \mathrm{~kg} \times 10 \mathrm{~ms}^{-2}=400 \mathrm{~N}[\because a=0]$ The rope will not break.
(d) When the monkey is falling freely, it would be a state of weightlessness. So, tension will be zero and the rope will not break.
$$
T-m g=m a
$$
where $\mathrm{T}$ represents the tension (figure a).
$$
\begin{array}{ll}
\therefore & T=m g+m a=m(g+a) \\
\text { or } & T=40 \mathrm{~kg}(10+6) \mathrm{ms}^{-2}=640 \mathrm{~N}
\end{array}
$$
But the rope can withstand a maximum tension of 600 N. So the rope will break.
(b) When the monkey is climbing down with an acceleration, then
$$
m g-T=m a \quad \text { (figure (b)) }
$$
$$
\Rightarrow T=m g-m a=m(g-a)
$$
or $\mathrm{T}=40 \mathrm{~kg}(10-4) \mathrm{ms}^{-2}=240 \mathrm{~N}$
The rope will not break.
(c) When the monkey climbs up with uniform speed, then $T=m g=40 \mathrm{~kg} \times 10 \mathrm{~ms}^{-2}=400 \mathrm{~N}[\because a=0]$ The rope will not break.
(d) When the monkey is falling freely, it would be a state of weightlessness. So, tension will be zero and the rope will not break.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.