A car of mass \(m\) moves in a horizontal circular path of radius \(r\). At any instant of time its speed is \(v\) and increasing at a rate of \(a\). Then, what is the total acceleration of car?
The maximum tension which an inextensible string of mass of mass \(0.1\)\(kgm^{-1}\) can withstand is \(10N\). The maximum velocity in \(ms^{-1}\) with which it can be rotated?
Ans: \(10\frac{m}{s}\).
A point P, moves in counter clockwise direction on a circular path. The movement of point P such that it sweeps out a length, \(s=t^{3}+5\), where; \(s\) is in meter and \(t\) is in seconds. The radius of the path is \(20m\). Find, the acceleration of point P when, \(t=2Sec\).
Ans: \(14\frac{m}{s^{2}}\).
For, a particle in uniform circular motion, the acceleration \(a\) at a point \(P\left(R,\theta\right)\) on the circular path of radius \(R\) can be given as?here; \(\vec{a}\) is directed radially inward, and \(\theta\) measured from x-axis.
Two cars of masses \(m_{1}\) and \(m_{2}\) are moving in circles of radii \(r_{1}\) and \(r_{2}\) respectively. Their speed is such that they make a complete circle in same time, \(t\). The ration of their centripetal acceleration?
Ans: \(r_{1}:r_{2}\).
Two objects of masses \(m_{1}\) and \(m_{2}\) are moving in circular paths of radii \(r_{1}\) and \(r_{2}\) respectively. Their speeds are such that they make complete circle in same time. Then, the ratio of force acting on them?
Ans: \(r_{1}:r_{2}\)
What is the approximate centripetal acceleration in gravitational unit of an air-craft flying at a speed of \(400ms^{-1}\) through a circular arc of radius \(0.6km\)? Take: \(\vec{g}=9.8ms^{-2}\).
Ans: \(26.7\frac{m}{s^{2}}\).
A vertical rod is rotated about its axis with a uniform angular speed \(\omega\). A simple pendulum of effective length \(l\) is attached to its upper end. What is its inclination with the rod?
A car of mass \(M\) passes over the top of a concave bridge with uniform speed \(V\), then the normal reaction acting on the car can be given as?
Ans: \(R=Mg+M\left(\frac{v^{2}}{r}\right)\).
A car of mass \(M\) passes over the top of a concave bridge with uniform speed \(V\), then the normal reaction acting on the car can be given by?
Ans: \(R=Mg-M\left(\frac{v^{2}}{r}\right)\).
A stone tied to a string is rotated with a uniform speed is a vertical plane. If, mass of the stone is \(m\), the length of the string is \(r\), the linear speed of the stone is \(v\). Then, what is the tension n the string when the stone is at (i) lowest and (ii) highest point will be?
Ans:(i) \(T_{L}=mg+\frac{mv^{2}}{r}\) and (ii) \(T_{H}=\frac{mv^{2}}{r}-mg\).
