(B) The maximum tension the string can withstand is $T_{\max} = mg = 50 \times 10 = 500 \ N$.For a mass $m$ rotating in a horizontal circle of radius

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$\frac{\sqrt{50}}{2 \pi} \text{ rps}$

(B) The maximum tension the string can withstand is $T_{\max} = mg = 50 \times 10 = 500 \ N$.For a mass $m$ rotating in a horizontal circle of radius $r$ with angular velocity $\omega$,the tension $T$ is given by $T = m \omega^2 r$.In this case,the length of the string $L = 10 \ m$ acts as the radius $r$ (assuming the string remains horizontal for the maximum speed case).Substituting $\omega = 2 \pi n$,where $n$ is the frequency in revolutions per second (rps):$T_{\max} = m (2 \pi n_{\max})^2 L$$500 = 1 \times (2 \pi n_{\max})^2 \times 10$$50 = (2 \pi n_{\max})^2$$2 \pi n_{\max} = \sqrt{50}$$n_{\max} = \frac{\sqrt{50}}{2 \pi} \text{ rps}$.

Class 11 Physics Newton's Laws of Motion and Friction Circular motion with Friction

Medium

$A$ string just breaks under a load of $50 \ kg$. $A$ mass of $1 \ kg$ is attached to one end of this string $10 \ m$ long and is rotated in a horizontal circle. Calculate the greatest number of revolutions that the mass can make in one second without breaking the string. (Take $g = 10 \ m/s^2$)

A
$\frac{2 \pi}{\sqrt{50}} \text{ rps}$
B
$\frac{\sqrt{50}}{2 \pi} \text{ rps}$
C
$\frac{\sqrt{55}}{2 \pi} \text{ rps}$
D
$\frac{\sqrt{60}}{2 \pi} \text{ rps}$

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Newton's Laws of Motion and Friction

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Circular motion with Friction

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$A$ string just breaks under a load of $50 \ kg$. $A$ mass of $1 \ kg$ is attached to one end of this string $10 \ m$ long and is rotated in a horizontal circle. Calculate the greatest number of revolutions that the mass can make in one second without breaking the string. (Take $g = 10 \ m/s^2$)

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On a dry road,the maximum speed of a vehicle along a circular path is $V$. When the road becomes wet,the maximum speed becomes $\frac{V}{2}$. If the coefficient of friction of the dry road is $\mu$,then the coefficient of friction of the wet road is:

$A$ car of mass $m$ moves on a banked road having radius $r$ and banking angle $\theta$. To avoid slipping from the banked road,the maximum permissible speed of the car is $v_0$. The coefficient of friction $\mu$ between the wheels of the car and the banked road is:

$A$ coin placed on a rotating table just slips when it is placed at a distance of $1\,cm$ from the center. If the angular velocity of the table is halved,it will just slip when placed at a distance of $............\,cm$ from the center.

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