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

Question

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 (A) 4 cm (B) 5 cm (C) 6 cm (D) 8 cm

Tardigrade Admin · Accepted Answer

When the acceleration of the blocks is same and constant

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 1 0^{- 2} m = 6 c m

4 cm

5 cm

6 cm

8 cm

When the acceleration of the blocks is same and constant Kx−32=7a...(1) 72−Kx=3a...(2) (1)÷(2),72−KxKx−32​=3a7a​ ⇒3(Kx−32)=7(72−Kx) 10Kx=7(72)+3(32);10(1000)x=600 ⇒x=6×10−2m=6cm