(D) Given: $\theta = 45^\circ$,$r = 0.4\,m$,$g = 10\,m/s^2$.For a conical pendulum,the forces acting on the bob are tension $T$ and weight $mg$.The ho

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(D) Given: $\theta = 45^\circ$,$r = 0.4\,m$,$g = 10\,m/s^2$.For a conical pendulum,the forces acting on the bob are tension $T$ and weight $mg$.The horizontal component of tension provides the necessary centripetal force:$T \sin \theta = \frac{mv^2}{r} \quad \dots(i)$The vertical component of tension balances the weight:$T \cos \theta = mg \quad \dots(ii)$Dividing equation $(i)$ by $(ii)$:$\tan \theta = \frac{v^2}{rg}$$v^2 = rg \tan \theta$Substituting the given values:$v^2 = 0.4 \times 10 \times \tan(45^\circ)$$v^2 = 4 \times 1 = 4$$v = \sqrt{4} = 2\,m/s$.

Class 11 Physics 2 Motion in a Plane Dynamics of circular Motion (Centrifugal force) and Pendulum and Motion on Curved path

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$A$ conical pendulum of length $1\,m$ makes an angle $\theta = 45^\circ$ with respect to the $Z$-axis and moves in a circle in the $XY$ plane. The radius of the circle is $0.4\,m$ and its centre is vertically below $O$. The speed of the pendulum,in its circular path,will be ..... $m/s$ (Take $g = 10\,ms^{-2}$)

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$0.4$
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$4$
C
$0.2$
D
$2$

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2 Motion in a Plane

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Dynamics of circular Motion (Centrifugal force) and Pendulum and Motion on Curved path

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EasyAP EAMCET 2020

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EasyAIPMT 1998

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MediumMHT CET 2009

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$A$ string of length $L$ is fixed at one end and carries a mass $M$ at the other end. The string makes $\frac{\pi}{2}$ revolutions per second around the vertical axis through the fixed end as shown in the figure. The tension in the string is:

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$A$ cyclist riding a bicycle at a speed of $14\sqrt{3} \text{ m/s}$ takes a turn around a circular road of radius $20\sqrt{3} \text{ m}$ without skidding. Given $g = 9.8 \text{ m/s}^2$,what is his inclination to the vertical in degrees?

$A$ 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 $25 \, N$. The maximum speed with which the ball can be moved is .......... $m/s$.

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