Question

A flat car is given an acceleration $a_o=2\text{m}/{\text{s}}^2$ starting from rest. A cable is connected to a crate $\text{A}$ of mass $50\text{kg}$ as shown in figure. Neglect friction between the floor and the car wheels and also the mass of the pulley. Calculate corresponding tension in the cable if $\mu =0.3$ between the crate and the floor of the car, considering equilibrium of crate.

(Assume friction is at its maximum value)

• A. $350\text{N}$
• B. $250\text{N}$
• C. $300\text{N}$
• D. $400\text{N}$

Answer 1

The correct option is B $250\text{N}$

We will work from the car frame. As car is in uniform acceleration, therefore it is non-inertial frame.

So, we will have to apply pseudo force on crate $\text{A}$ of magnitude $m{a}_o$ in opposite direction of $a_o$.

Tension$\left(T\right)$ on it due to cable will try to move it forward. Hence, friction on it will be acting backward.

FBD of crate $\text{A}$ is given by,


For equilibrium, $T=m{a}_o+f$

$T=m{a}_o+\mu mg$

$\Rightarrow T=m(a_o+\mu g)$

Substituting the values, we get

$T=50(2+0.3\times 10)$

$\therefore T=250\text{N}$

Hence, option $\left(B\right)$ is correct.