Question

If m_1 < m_2 and the floor is smooth. If the car accelerates towards right:

• Rope will be under tension
• Rope will be slack

Solution

There is friction between m_1 and m_2 which helps in accelerating.

We can solve it using 2 methods.

First suppose the rope is under tension. Let T be the tension in the string, F be the friction between m_1 and m_2

So on m_1:

m_1 a=T+F

On m_2

m_2 a=F-T

So T= (m_1-m_2)a

But m_1 < m_2 so T<0 which is not possible since it is rope.

Method 2:

Since the same frictional force is acting on m_1,m_2. But m_1 < m_2 and the same tension is acting on m_1,m_2. So the acceleration of m_1 > m_2, hence the rope will be slack and there will be no tension in the rope.