You visited us 5 times! Enjoying our articles? Unlock Full Access!

Com of Solid Bodies

In the arrang...

Question

In the arrangement, shown in figure, pulleys are massless and frictionless and threads are inextensible block of mass $m_{2}$ will remain at rest if.

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

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

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

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

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

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

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

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

Open in App

Solution

The correct option is B $\frac{4}{m_{1}} = \frac{1}{m_{2}} + \frac{1}{m_{3}}$
Let, the tension in string connected to $m_{1}$ is $T$ and $m_{2}$ and $m_{3}$ is $T_{1}$ .

$T = m_{1} g$
$2 T_{1} = T$
$T_{1} = \frac{T}{2}$

let, the acceleration of the mass $m_{2}$ be
$m_{2} g - T_{1} = m_{2} a$ ......(I)
$T_{1} - m_{3} g = m_{3} a$ ......(II)

After solving,

$m_{2} g - m_{3} g = (m_{2} + m_{3}) a$
$g (m_{2} - m_{3}) = (m_{2} + m_{3}) a$

Now,

$a = \frac{g (m_{2} - m_{3})}{m_{2} + m_{3}}$

Now, put the value of $a$ in equation (II)

$T_{1} - m_{3} g = m_{3} (\frac{g (m_{2} - m_{3})}{m_{2} + m_{3}})$

$T_{1} = m_{3} \frac{g (m_{2} - m_{3})}{m_{2} + m_{3}} + m_{3} g$

$T_{1} = m_{3} g (\frac{2 m_{2}}{m_{2} + m_{3}})$

$T_{1} = \frac{2 m_{2} m_{3} g}{m_{2} + m_{3}}$

Now, put the value of $T_{1}$

$\frac{T}{2} = \frac{2 m_{2} m_{3} g}{m_{2} + m_{3}}$

$T = \frac{4 m_{2} m_{3} g}{m_{2} + m_{3}}$

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

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

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

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

Therefore the block of mass $m_{2}$ at rest if $\frac{4}{m_{1}} = \frac{1}{m_{3}} + \frac{1}{m_{2}}$

Suggest Corrections

Similar questions

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. Q. RBI publishes figures for four alternative measures of money supply, viz.

M 1, M 2, M 3

and

M 4

. Arrange them in decreasing order of their liquidity:

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. Three blocks are connected on a horizontal frictionless table by two light strings, one between

m_{1}

and

m_{2}

, another between

m_{2}

and

m_{3}

. The tensions are

T_{1}

between

m_{1}

and

m_{2}

and

T_{2}

between

m_{2}

and

m_{3}

. if

m_{1}

= 1 kg ,

m_{2}

= 8 kg,

m_{3}

= 27 kg and F = 36 N applied on

m_{3}

, then

T_{2}

will be

Join BYJU'S Learning Program

In the arrangement, shown in figure, pulleys are massless and frictionless and threads are inextensible block of mass m2 will remain at rest if.

In the arrangement, shown in figure, pulleys are massless and frictionless and threads are inextensible block of mass $m_{2}$ will remain at rest if.