Physics Q29 – JEE-MAIN 2026

Home Physics Laws of MotionQuestion #214

Three masses

m_{1} = 4

kg,

m_{2} = 4

kg and

m_{3} = 6

kg are suspended from a fixed smooth frictionless pulley as shown in the figure below. The value of

T_{1} / T_{2}

is _______ (take

g = 10

m/s

^{2}

)

Clue 1 of 3: Identify the System

Recognize the two main blocks of mass connected by the main string over the pulley.

🧠 Full Solution Path

Step 1: Determine System Acceleration✦ Active

Identify the effective masses on each side of the pulley. On the left, $M_{L} = m_{1} = 4$ kg. On the right, $M_{R} = m_{2} + m_{3} = 4 + 6 = 10$ kg. Since $M_{R} > M_{L}$ , the system accelerates such that $M_{R}$ moves down and $M_{L}$ moves up. The acceleration $a$ of the system is given by:

a = \frac{(M_{R} - M_{L})}{(M_{R} + M_{L})} g

Substitute the given values ( $g = 10$ m/s $^{2}$ ):

a = \frac{(10 - 4)}{(10 + 4)} \times 10 = \frac{6}{14} \times 10 = \frac{30}{7} {m/s}^{2}

Step 2: Calculate Tension

T_{1}

○ Expand

Tension $T_{1}$ is in the main string. Consider the forces on mass $m_{1}$ . It is accelerating upwards. Applying Newton's second law:

T_{1} - m_{1} g = m_{1} a

Solve for $T_{1}$ :

T_{1} = m_{1} (g + a) = 4 (10 + \frac{30}{7}) = 4 (\frac{70 + 30}{7}) = 4 (\frac{100}{7}) = \frac{400}{7} N

💡 Teacher's Secret Hint

Remember to consider the direction of acceleration when setting up the force equations.

Step 3: Calculate Tension

T_{2}

and the Ratio

T_{1} / T_{2}

○ Expand

Tension $T_{2}$ is in the string connecting $m_{2}$ and $m_{3}$ . Consider the forces on mass $m_{3}$ . It is accelerating downwards with acceleration $a$ . Applying Newton's second law:

m_{3} g - T_{2} = m_{3} a

Solve for $T_{2}$ :

T_{2} = m_{3} (g - a) = 6 (10 - \frac{30}{7}) = 6 (\frac{70 - 30}{7}) = 6 (\frac{40}{7}) = \frac{240}{7} N

Finally, calculate the ratio $T_{1} / T_{2}$ :

\frac{T_{1}}{T_{2}} = \frac{\frac{400}{7}}{\frac{240}{7}} = \frac{400}{240} = \frac{40}{24} = \frac{5}{3}

💡 Teacher's Secret Hint

Ensure you apply Newton's second law correctly for each mass, considering its direction of motion.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.

Physics Question 29 – JEE-MAIN 2026

Clue 1 of 3: Identify the System

🧠 Full Solution Path