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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

281449_cc4a474e808f4d85a4829f816429c11d.png


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

The correct option is A b, c
Let 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 $$9.8m{s}^{-2}$$)

720568_281449_ans_ab0e38013c50490b9a2a8ad3aedb9ad1.png

Physics

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