Question

Mass of block $A$ is $1\text{kg}$ and that of block $B$ is $2\text{kg}$. If a horizontal force $F=10\text{N}$ is applied on the pulley, find the acceleration of block $A$ and block $B$ respectively. All surfaces are frictionless.

• A. $2.5{\text{m/s}}^2,5{\text{m/s}}^2$
• B. $5{\text{m/s}}^2,3{\text{m/s}}^2$
• C. $5{\text{m/s}}^2,2.5{\text{m/s}}^2$
• D. $\text{None of these}$

Answer 1

The correct option is C $5{\text{m/s}}^2,2.5{\text{m/s}}^2$


From FBD of pulley,
$2T=10\text{N}$
$\Rightarrow T=5\text{N}$


Now, from FBD of block $A$, we get
$m_A{a}_A=5\text{N}$
$\Rightarrow a_A=5{\text{m/s}}^2$

Again, from FBD of block $B$, we get
$m_B{a}_B=5\text{N}$
$\Rightarrow 2\times a_B=5\text{N}$
$\Rightarrow a_B=2.5{\text{m/s}}^2$