Question

A block of mass $m_1=2kg$ on a smooth inclined plane at angle ${30}^o$ is connected to a second block of mass $m_2=3kg$ by a cord passing over a frictionless pulley as shown in fig. The acceleration of each block is (assume $g=10m/se{c}^2)$:

• A. $2m/se{c}^2$
• B. $4m/se{c}^2$
• C. $6m/se{c}^2$
• D. $8m/se{c}^2$

Answer 1

The correct option is B $4m/se{c}^2$

let tension be $T$ and acceleration $a$ of the blocks

for block 1 eq. of tension is

$T-m_{1}gsin{30}^o=m_{1}a$

$T=m_1(gsin{30}^o+a)$

for block 2 eq. of tension is

$m_{2}g-T=m_{2}a$

$T=m_2(g-a)$

equating above equations

$m_1(gsin{30}^o+a)=m_2(g-a)$

$a=\frac{m_{2}g-m_{1}gsin{30}^o}{m_1+m_2}$

$a=4m/se{c}^2$