Question

In the system shown in figure all surfaces are smooth, string
is massless and inextensible. (in steady state) Find the
(a) acceleration of the system
(b) tension in the string and
(c) extension in the spring if force constant of spring
is k 50 N/m (Take g=10 m/s2)
​

Answer 1

Answer:

b option tension in the string

Answer 2

Answer:

Acceleration of a system is $\frac{50}{6} m/s^{2}$ and tension in the string is $\frac{50}{6}$ N and the extension in the spring is 0.1 m/s

Explanation:

Acceleration of a system = $\frac{F_{net} }{m}$

= $\frac{m_{B}g +m_{C}g }{2 +3+1}$

= $\frac{2(10)+3(10)}{6}$

= $\frac{50}{6} m/s^{2}$

Tension in the string

For block A

Tension = ma

m= mass

a = acceleration

Tension(T) = 1 ×$\frac{50}{6}$

T = $\frac{50}{6}$ N

Extension in the spring if force constant of spring k = 50N

Therefore,

⇒30 - kx = 3a

⇒ 30 - 50(x) = 3 (50/6)

⇒ 30-50x = 25

⇒ 30 - 25 = 50x

⇒ 5 = 50x

5/50 =x

x = 0.1 m/s

Final answer:

Acceleration of a system is $\frac{50}{6} m/s^{2}$ and tension in the string is $\frac{50}{6}$ N and the extension in the spring is 0.1 m/s

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