Question

In the arrangement shown in the figure, $m_A=1\text{kg},m_B=4\text{kg}$. String is light and inextensible while pulley is smooth. Coefficient of friction between the block $A$ and the table is $\mu =0.2$. Find the speed of both the blocks when block $B$ has descended by a height $h=1\text{m}$. ( Take $g=10{\text{m/s}}^2$).

• A. $3.5\text{m/s}$
• B. $3.9\text{m/s}$
• C. $4.5\text{m/s}$
• D. $3.6\text{m/s}$

Answer 1

The correct option is B $3.9\text{m/s}$

From constraint relation,
$v_A=v_B=v$ (say)
Friction between block $A$ and table will be $f=\mu m_{A}g=\left(0.2\right)\left(1\right)\left(10\right)=2\text{N}$

When block B descends by height $h$, block A moves horizontally by same distance.
From work-energy theorem;
$W_{non-cons}=\Delta U+\Delta K.E$
$⟹-fh=-m_{B}gh+\frac{1}{2}(m_A+m_B)v^2$
$⟹(-2)\left(1\right)=-\left(4\right)\left(10\right)\left(1\right)+\frac{1}{2}(1+4)v^2$
$⟹-2=(-40)+\left(2.5\right)v^2$
$⟹v^2=15.2$
$⟹v=3.9\text{m/s}$