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  4. Two blocks of masses 7 kg and 3 kg are connected by a spring of stiffness 1000 Nm -1 and placed on a smooth horizontal surface. They are acted by horizontal forces of 72 N and 32 N in opposite directions as shown in the figure. When acceleration of the blocks are equal and constant, the extension of the spring is

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Q. Two blocks of masses $7\, kg$ and $3 \,kg$ are connected by a spring of stiffness $1000\, Nm ^{-1}$ and placed on a smooth horizontal surface. They are acted by horizontal forces of $72\, N$ and $32 N$ in opposite directions as shown in the figure. When acceleration of the blocks are equal and constant, the extension of the spring isPhysics Question Image

Laws of Motion

Solution:

When the acceleration of the blocks is same and constant
image
$K x-32=7 a \,\,\,\,\,\, ...(1)$
$72-K x=3 a \,\,\,\,\,\,... (2)$
$(1) \div(2), \frac{K x-32}{72-K x}=\frac{7 a}{3 a}$
$\Rightarrow 3(K x-32)=7(72-K x)$
$10 K x=7(72)+3(32) ; 10(1000) x=600$
$\Rightarrow x=6 \times 10^{-2} m =6 cm$