Question

In the arrangement shown in figure $$m_1 = 8kg, m_2 = 2kg$$ and spring constant $$K = 1600 N/m$$. All surfaces are smooth then:[a] Tension in string, T = 17.2N[b] Tension in string, T = 15.68 N[c] Extension in spring is 9.8 mm[d] Extension in spring is 12 mm

A
b, c
B
b, d
C
a, c
D
a, d

Solution

The correct option is A b, cLet the tension generated in the string be $$T$$.This string is connected to the spring so tension becomes equal to$$Kx$$, where $$x$$ is the elongation in the spring.Now,equation of motion are as follows-$${m}_{2}g-kx={m}_{2}a$$$$kx={m}_{1}a$$.solvingthese equations give $$kx=15.68N$$,which is equal to the tension produced $$T$$.Also $$x$$ comes out to be $$9.8mm$$.(Value of $$g$$ is $$9.8m{s}^{-2}$$)Physics

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