Two blocks $m_{1}$ and $m_{2}$ , are acted upon by the forces $F_{1}$ and $F_{2}$ as shown in the fig. If there is no relative sliding between the blocks and the ground is smooth, find the magnitude of static friction between the blocks.Make necessary assumptions.

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

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

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

Open in App

Solution

The correct option is C

As there is no sliding between the blocks the friction will be static. Assuming the frictional forces on $m_{1}$ as f( $\leftarrow$ ) and $m_{2}$ as f( $\to$ ), we have drawn the Free body diagram without normal reactions and weights.

Referring to Free body diagram as shown in figure, we have the following equations of motion.

For m₁:

$F_{1}$ - f = $m_{1}$ $a_{1}$ . . . . . . (i)

For $m_{2}$ : $F_{2}$ + f = $m_{2}$ $a_{2}$ . . . . . . (ii)

Since the friction is static, $a_{1}$ = $a_{2}$

Substituting $a_{1} f r o m e q u a t i o n (i) a_{2} f r o m e q u a t i o n (i i) i n ‘ e q u a t i o n (i i i), w e h a v e \frac{F_{1} - f}{m_{1}} = \frac{F_{2} + f}{m_{2}}$

This gives f = $\frac{m_{2} F_{1} - m_{1} F_{2}}{m_{1} + m_{2}}$

case(ii)

Friction on $m_{1} i s a c t i n g i n r i g h t w a r d d i r e c t i o n .$

For $m_{1} : F_{1} + f = m_{1} a_{1} a n d f o r m_{2} : F_{2} - f = m_{2} a_{2}$

As static, $a_{1} = a_{2}$

$∴ \frac{F_{1} + f}{m_{1}} = \frac{F_{2} - f}{m_{2}}$

$\Rightarrow f = \frac{m_{1} F_{2} - m_{2} F_{1}}{m_{1} + m_{2}}$
$∴ M a g n i t u d e o f f = \frac{m_{2} F_{1} - m_{1} F_{2}}{m_{1} + m_{2}}$

Suggest Corrections

Similar questions

Q. In Fig. Block

m_{2}

is located on block

m_{1}

. If there is no relative sliding between the blocks and the plane is smooth, find the friction force between the blocks.

Q. In the figure, block

m_{1}

is loaded on block

m_{2}

. If there is no relative sliding between the blocks and the inclined plane is smooth, the frictional force acting between the blocks is:

The block $m_{1}$ is loaded on the block $m_{2}$ . If there is no relative sliding between the blocks and the inclined plane is smooth, find the friction force between the blocks.

Q. In the figure, block

m_{1}

is loaded on block

m_{2}

. If there is no relative sliding between the blocks and the inclined plane is smooth, the frictional force acting between the blocks is:

The block $m_{1}$ is loaded on the block $m_{2}$ . If there is no relative sliding between the blocks and the inclined plane is smooth, find the friction force between the blocks.

Join BYJU'S Learning Program

Two blocks m1and m2, are acted upon by the forces F1 and F2 as shown in the fig. If there is no relative sliding between the blocks and the ground is smooth, find the magnitude of static friction between the blocks.Make necessary assumptions.

Two blocks $m_{1}$ and $m_{2}$ , are acted upon by the forces $F_{1}$ and $F_{2}$ as shown in the fig. If there is no relative sliding between the blocks and the ground is smooth, find the magnitude of static friction between the blocks.Make necessary assumptions.