Question

Two blocks of masses $5kg$ and $2kg$ (see fig.) are initially at rest on the floor. They are connected by a light string, passing over a light friction less pulley. An upward force F is applied on the pulley and maintained constant. Calculate the acceleration $a1$ and $a2$ of the $5kg$ and $2kg$ masses, respectively, when $F$ is $110N$ $(g=10m{s}^{-2}).$

• A. 0, 2.5 $m{s}^{-2}$
• B. $1m{s}^{-2},17.5m{s}^{-2}$
• C. 2.5 $m{s}^{-2}$, 2.5 $m{s}^{-2}$
• D. 1 $m{s}^{-2}$, 2.5 $m{s}^{-2}$

Answer 1

The correct option is B $1m{s}^{-2},17.5m{s}^{-2}$

the block will be lifted only when the tension of string exceeds the gravitational pull on them.

$gravitationalforce=mg+Mg$

$=2kg\times 10m/s²+5kg\times 10m/s²=70N$

Let's check , $F-2T=0$ [ see free body diagram as shown in figure ]

given, $F=110N$

$110-2T=0=>T=55N$

tension is greater than gravitational pull { e.g., $55N>50N$ and $55N>20N$}

so, use Newton's law of motion separately for both blocks

acceleration of block of mass $2kg$ is $a$ ,

$T-mg=ma$

$55-2\times 10=2\times a$

$55-20=2a=>a=17.5m/s²$

acceleration of block of mass $5kg$ is $a^{\prime },$

$T-Mg=M{a}^{\prime }$

$55-5\times 10=5a$

$55-50=5a=>a=1m/s²$

Hence,

option $B$ is correct answer.