Question

A block of metal of mass 2kg on a horizontal table is attached to a mass of 0.45 kg by a light string passing over a frictionless pulley at the edge of the table. The block is subjected to a horizontal force by allowing the 0.45 kg mass to fall. The coefficient of sliding friction between the block and table is 0.2, the acceleration of system and the distance the block would continue to move if, the string breaks after 2 sec. of motion are

• A. $0.2m/s^2,4.1cm$
• B. $0.2m/s^2,44.4cm$
• C. $0.4m/s^2,4.1cm$
• D. $0.4m/s^2,2.1cm$

Answer 1

The correct option is A $0.2m/s^2,4.1cm$

Given-
$m_1=0.45kg$
$m_2=2kg$
$\mu =0.2$
Initial acceleration-
$a=\frac{(m_1-\mu m_2)g}{(m_1+m_2)}$
or, $a=\frac{(0.45-0.2\times 2)g}{(0.45+2)}$
or, $a=0.2m/s^2$
Tension in the string-
$T=\mu m_{2}g+m_{2}a$
or, $T=0.2\times 2\times 9.8+2\times 0.2$
or, $T=4.32N$
Stopping distance-
$s=\frac{u^2}{2\mu g}$ ($\because u=at)$
or, $s=\frac{\left({0.4}^2\right)}{(2\times 0.2\times 9.8)}$
or, $s=0.0408m$
or, $s=4.08cm$

The correct answer is $0.2m/s^2,4.1cm$