KCET · Physics · Laws of Motion

Two masses of \(5 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) are suspended with the help of massless inextensible strings as shown in figure below.

When whole system is going upwards with acceleration \(2 \mathrm{~m} / \mathrm{s}^2\), the value of \(T_1\) is (use, \(g=9.8 \mathrm{~m} / \mathrm{s}^2\) )

A \(35.4 \mathrm{~N}\)
B \(23.6 \mathrm{~N}\)
C \(59 \mathrm{~N}\)
D \(94.4 \mathrm{~N}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(94.4 \mathrm{~N}\)

Step-by-step Solution

Detailed explanation

The given situation is shown below

Equation of motion for body \(m_2\),
\(T_2-m_2 g =m_2 a \)
\(T_2-3 g =3 \times 2 \)
\(T_2 =3 g+6=3 \times 9.8+6=35.4 \mathrm{~N}\) Equation of motion of mass of \(5 \mathrm{~kg}\),
\(T_1-T_2-m_1 g =m_1 a \)
\(\Rightarrow T_1-35.4-5 \times 9.8 =5 \times 2 \)
\(\Rightarrow T_1-84.4 =10^{\circ} \)
\(\Rightarrow T_1 =10+84.4=94.4 \mathrm{~N}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Two masses of \(5 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) are suspended with the help of massless inextensible strings as shown in figure below.When whole system is going upwards with acceleration \(2 \mathrm{~m} / \mathrm{s}^2\), the value of \(T_1\) is (use, \(g=9.8 \mathrm{~m} / \mathrm{s}^2\) )

Step-by-step Solution

Two masses of \(5 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) are suspended with the help of massless inextensible strings as shown in figure below.

When whole system is going upwards with acceleration \(2 \mathrm{~m} / \mathrm{s}^2\), the value of \(T_1\) is (use, \(g=9.8 \mathrm{~m} / \mathrm{s}^2\) )