Question

A block P of mass 10 kg is lying on a rough
horizontal table and another block Q hangs
vertically with the help of ideal string as shown in the
figure. If coefficient of friction between the table and
block is 0.4, then maximum mass of block Q for
which the system will be stationary is

(1) 6 kg
(3) 8 kg
(2) 8 kg
(4) 2 kg​

Answer 1

Given:

A block P of mass 10kg is lying on a rough horizontal table

block Q hangs vertically with the help of ideal string

coefficient of friction between table and block is 0.4

To Find:

Maximum mass of block Q for which the system will be stationary

Solution:

Free body diagram of block P

$\mu N (-x direction)\\Tension T (+ x direction)$

F(net) = 0

T = .4(N)

force in vertical direction

N = mg   (take g = 10)

T = .4(10)(10)= 40 N

resolve tension in the inclined spring in vertical and horizontal direction

T sin45 = Mg

T = $\frac{Mg}{sin 45}$

$M = \frac{ Tsin 45}{g}\\ M = 2.82 kg$

Mass of block Q is 2.82 kg