A block of mass $m_{2}$ is placed on a horizontal table and another block of mass $m_{1}$ is placed on top of it. An increasing horizontal force $F = α t$ is exerted on the upper block but the lower block never moves as a result. If the co-efficient of friction between the blocks is $μ_{1}$ and the between the lower block and the table is $μ_{2}$ , then what is the maximum possible value of $μ_{1} / μ_{2}$ ?

\frac{m_{2}}{m_{1}}

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

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

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

\frac{m_{1}}{m_{2}}

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

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

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

Open in App

Solution

The correct option is A $1 + \frac{m_{2}}{m_{1}}$
$f_{2} =$ acting friction between lower block & the table.
$f_{1} =$ acting friction between lower block & upper block.
$∵ m_{2}$ never moves.
So $f_{1} \leq f_{2}$ 1
So friction acting in between the block is always less than or equal to friction acting between lower block & table.
So $μ_{1} m_{1} g \leq μ_{2} (m_{1} + m_{2}) g$
$\frac{μ_{1}}{μ_{2}} \leq \frac{m_{1} + m_{2}}{m_{1}}$
$\frac{m u_{1}}{μ_{2}} \leq 1 + \frac{m_{2}}{m_{1}}$
So maximum value of $\frac{μ_{1}}{μ_{2}} = 1 + \frac{m_{2}}{m_{1}}$ .

Suggest Corrections

Similar questions

Consider two blocks of masses m₁and m₂ placed in contact with each other on a friction less horizontal surface. Let a force F be applied on block of mass m₁, then the value of contact force between the blocks is

Q. Two blocks of masses

M_{1}

and

M_{2}

are connected with a string passing over a pulley as shown in the figure. The block

M_{1}

lies on a horizontal surface. The coefficient of friction between the block

M_{1}

and the horizontal surface is

μ

. The system accelerates. What additional mass

m

should be placed on the block

M_{1}

so that the system does not accelerate?

A block A of mass m₁ rests on a horizontal table. A lights string connected to it passes over a frictionless pulley at the edge of table and from its other end another block B of mass m₂ is suspended. The coefficient of kinetic friction between the block and the table is . When the block A is sliding on the table, the tension in the string is :