Question

3. Find the value of F for which two block of mass m and 2m [as shown in the figure (in the end)]

remain at rest with respect to 4m. [All the interface are friction less]
pls help me guys!!!​

Answer 1

If F is the applied force then acceleration of the system is –:

$\rm \frac{F}{2m + m} = \frac{F}{3m}$

Now when we apply the force from the left, the force applied on the block m is –:

$\rm \frac{F}{3m} \: m = \frac{F}{3}$

This will be the force in the contact.

When we apply the force from the right from on the block will be –:

$\implies \sf\frac{F}{3m} \: \: 2m\ = \frac{2F}{3}$

this will be the force on the contact then.So the ratio is

$\sf \binom{F}{3} : \binom{2F}{3} = 1:2$