You visited us 131 times! Enjoying our articles? Unlock Full Access!

Distance

Three masses ...

Question

Three masses $m_{1}, m_{2}$ and $m_{3}$ are attached to a string pulley system as shown. All three masses are held at rest and then released. To keep $m_{3}$ at rest, the condition is:

\frac{1}{m_{3}} = \frac{1}{m_{1}} + \frac{1}{m_{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

m_{1} + m_{2} = m_{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{4}{m_{3}} = \frac{1}{m_{1}} + \frac{1}{m_{2}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{1}{m_{1}} + \frac{2}{m_{2}} + \frac{3}{m_{3}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $\frac{4}{m_{3}} = \frac{1}{m_{1}} + \frac{1}{m_{2}}$
Let tension produced string consisting of $m_{3}$ be $T$ .Since $m_{3}$ has to be at rest, $T$ should be equal to $m_{3} g$ .Now consider the lower pulley.Forces acting on this pulley are $T_{1}$ on one string and $T_{1}$ o the other string.Since tis pulley is at rest so
$2 T_{1} = T$ and $T_{1} = \frac{T}{2}$ .
Now take acceleration of $m_{2}$ as $a$ downwards and $m_{3}$ as $a$ upwards.
Equation of motion of these two blocks are given,
$\frac{T}{2} - m_{1} g = m_{1} a ⟶ 1$
$- \frac{T}{2} + m_{2} g = m_{2} a ⟶ 2$
divide $e q .1$ by $e q .2$ and rearrange the divided equations to get
${\frac{4}{m}}_{3} = {\frac{1}{m}}_{1} + {\frac{1}{m}}_{2}$ , $i . e .$ option $c$ .

Suggest Corrections

Similar questions

Q. Three masses

m_{1}

m_{2}

and

m_{3}

are attached to a string as shown in the figure. All three masses are held at rest and then released. To keep

m_{3}

at rest the condition is

Q. In the arrangement, shown in figure, pulleys are massless and frictionless and threads are inextensible. Blocks of mass m1 will remain at rest if

Three solids of masses $m_{1}, m_{2} a n d m_{3}$ are connected with weightless string in succession and are placed on a frictionless table. If the mass $m_{3}$ is dragged with a force T, the tension in the string between $m_{2}$ and $m_{3}$ is

Q. In the figure, pulleys are smooth and strings are massless

m_{1} = 1 k g

and

m_{2} = \frac{1}{3} k g

. To keep

m_{3}

at rest,

m_{3}

should be

Q. Let

m_{1} = 1 k g, m_{2} = 2 k g

and

m_{3} = 3 k g

in figure. Find the accelerations of

m_{1}, m_{2}

and

m_{3}

. The string from the upper pulley to

m_{1}

20 c m

when the system is released from rest. How long will it take before

m_{1}

strikes the pulley?

Join BYJU'S Learning Program

Three masses m1,m2 and m3 are attached to a string pulley system as shown. All three masses are held at rest and then released. To keep m3 at rest, the condition is:

Three masses $m_{1}, m_{2}$ and $m_{3}$ are attached to a string pulley system as shown. All three masses are held at rest and then released. To keep $m_{3}$ at rest, the condition is: