CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Acceleration

If the pulley...

Question

If the pulley is massless and moves with an upward acceleration $a_{o}$ , find the acceleration of block $m_{1}$ w.r.t elevator.

A

\frac{(m_{2} - m_{1}) (g - a_{o})}{(m_{1} + m_{2})}

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

B

\frac{(m_{2} - m_{1}) (g + a_{o})}{(m_{1} + m_{2})}

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

C

\frac{(m_{2} - m_{1}) g}{m_{1}}

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

D

\frac{(m_{2} - m_{1}) a_{o}}{m_{1}}

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

Open in App

Solution

The correct option is B $\frac{(m_{2} - m_{1}) (g + a_{o})}{(m_{1} + m_{2})}$

Let the acceleration of block $m_{1}$ w.r.t the pulley be $a$ (upward) and the acceleration of $m_{2}$ w.r.t the pulley be $a$ (downward).
$∴$ Equation for $m_{1}$ :
$T - m_{1} g = m_{1} a_{1}$
where $a_{1} = a_{0} + a$
So, $T - m_{1} g = m_{1} (a_{0} + a) . . . . . (1)$

Now, equation for $m_{2}$ :
$T - m_{2} g = m_{2} a_{2}$
where $a_{2} = (a_{0} - a)$
Therefore, $T - m_{2} g = m_{2} (a_{0} - a) . . . . . . (2)$

Solving both equations $(1)$ & $(2)$ , we get
$m_{1} (a_{0} + a) + m_{1} g - m_{2} g = m_{2} (a_{o} - a)$
$\Rightarrow a (m_{1} + m_{2}) = (m_{2} - m_{1}) (g + a_{o})$
$\Rightarrow a = [\frac{m_{2} - m_{1}}{m_{1} + m_{2}}] (g + a_{0})$

Suggest Corrections

thumbs-up

0

Similar questions

Q. If the pulley is massless and moves with an upward acceleration

a_{0}

, find the acceleration of

m_{1}

m_{2}

w.r.t. to elevator.

Q. If the pulley is massless and moves with an upward acceleration

a_{o}

, find the acceleration of block

m_{1}

w.r.t elevator.

Q. An arrangement of pulley, string and blocks is shown in figure. Given

m_{1} = 4 kg, m_{2} = 2 kg

m_{3} = 4 kg

. All surfaces are frictionless, string and pulleys are massless. Find the acceleration of block

m_{1}

g = 10 {m/s}^{2}

Q. Three blocks of mass

m_{1} = 4 k g, m_{2} = 2 k g, m_{3} = 4 k g

are connected as shown in figure. All surfaces are smooth and pulley is massless, find the acceleration of mass

m_{1}

?

Two blocks of masses $m_{1} = 2$ kg and $m_{2} = 4$ kg hang over a massless pulley as shown in figure. A force F0 = 100N acting at the axis of the pulley accelerates the system upward. Then

Join BYJU'S Learning Program

explore_more_icon

Explore more

Standard XIII Physics

Join BYJU'S Learning Program

CrossIcon