Question

A smooth pulley fixed to a frictionless axle carries two masses attached to a massless inextensible string as shown in figure. If the tension in the string is 45 N, the mass M is
\([M\lt 6\text{kg},\text{ take }g=10\text{ m/s}^{2}]\)

• A. \(5.6\text{ kg}\)
• B. \(5\text{ kg}\)
• C. \(4.2\text{ kg}\)
• D. \(3.6\text{ kg}\)

Hint:

Apply Newton's second law to both masses with the same acceleration and the given tension.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
The figure shows \(M\) and a \(6\text{ kg}\) block over a smooth pulley. Since \(M<6\text{ kg}\), the heavier block moves down and \(M\) moves up with the same acceleration.

Step 2: Heavier block
\(6g-T=6a\Rightarrow 60-45=6a\Rightarrow a=2.5\text{ m/s}^2\)

Step 3: Lighter block
\(T-Mg=Ma\Rightarrow 45=M(10+2.5)\)

Step 4: Solve for M
\(M=\dfrac{45}{12.5}=3.6\text{ kg}\)

Final Answer:
The mass \(M\) is \(3.6\text{ kg}\). \[ \boxed{\text{(D) }3.6\text{ kg}} \]