Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved?

14 m/s

3 m/s

3.92 m/s

5 m/s

Step-by-Step Solution

Identify the Force: For a body moving in a horizontal circle attached to a string, the centripetal force required to maintain the circular path is provided by the tension ( $T$ ) in the string [Source 62, 68].
Formula: The centripetal force is given by $F_c = \frac{mv^2}{r}$ . Thus, $T = \frac{mv^2}{r}$ .
Condition for Breaking: The string breaks if the tension exceeds the maximum tension ( $T_{max}$ ). To find the maximum speed ( $v_{max}$ ), we equate the tension to the breaking limit. $T_{max} = \frac{m v_{max}^2}{r}$
Calculation:

Mass ( $m$ ) = 0.25 kg
Radius ( $r$ ) = Length of string = 1.96 m
Max Tension ( $T_{max}$ ) = 25 N $25 = \frac{0.25 \times v_{max}^2}{1.96}$ $v_{max}^2 = \frac{25 \times 1.96}{0.25} = 100 \times 1.96 = 196$ $v_{max} = \sqrt{196} = 14 \text{ m/s}$

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