Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

A monkey of mass $20 \text{ kg}$ is holding a vertical rope. The rope will not break when a mass of $25 \text{ kg}$ is suspended from it but will break if the mass exceeds $25 \text{ kg}$ . What is the maximum acceleration with which the monkey can climb up along the rope ( $g = 10 \text{ m/s}^2$ )?

$10 \text{ m/s}^2$

$25 \text{ m/s}^2$

$2.5 \text{ m/s}^2$

$5 \text{ m/s}^2$

Step-by-Step Solution

Determine Maximum Tension ( $T_{max}$ ): The breaking strength of the rope corresponds to the weight of the maximum mass it can hold ( $M = 25 \text{ kg}$ ). Thus, the maximum tension is: $T_{max} = M \cdot g = 25 \text{ kg} \times 10 \text{ m/s}^2 = 250 \text{ N}$
Apply Newton's Second Law: For the monkey (mass $m = 20 \text{ kg}$ ) climbing upwards with acceleration $a$ , the forces are Tension ( $T$ ) acting upwards and Weight ( $mg$ ) acting downwards. The equation of motion is: $T - mg = ma$ [Source 118, 126]
Solve for Maximum Acceleration ( $a_{max}$ ): Substitute $T_{max}$ into the equation: $250 \text{ N} - (20 \text{ kg} \times 10 \text{ m/s}^2) = 20 \text{ kg} \times a_{max}$ $250 - 200 = 20 \cdot a_{max}$ $50 = 20 \cdot a_{max}$ $a_{max} = \frac{50}{20} = 2.5 \text{ m/s}^2$

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