Question

For the spring block arrangement as shown in figure:


Given that $k_1=2k_2$. If force applied by the first spring on the block is $F_1$ and force applied by the second spring on the block is $F_2$, choose the correct option(s) if the block is in equilibrium with the action of an external force $30\text{N}$ on the block.

• A. $x_1=2x_2$
• B. $x_1=x_2$
• C. $F_1=F_2=30\text{N}$
• D. $F_1=20\text{N},F_2=10\text{N}$

Answer 1

Answer: (B), (D)

The correct options are
B $x_1=x_2$
D $F_1=20\text{N},F_2=10\text{N}$

Let $1^{\text{st}}$ spring be stretched by distance $x_1$ and $2^{\text{nd}}$ spring be stretched by distance $x_2$
$\because$ Both springs are connected in parallel, $x_1=x_2$
Applying equilibrium condition on block gives,
$F_1+F_2=F\dots \left(1\right)$
Now,
$F_1=k_1{x}_1$
$F_2=k_2{x}_2$

From (1) $\Rightarrow 30=k_1{x}_1+k_2{x}_2$
[$\because k_1=2k_2$]
$\Rightarrow 30=3k_2{x}_2=3F_2$
$\therefore F_2=10\text{N}$

$F_1=k_1{x}_1=2k_2{x}_2=2F_2$
$\therefore F_1=2\times 10=20\text{N}$