A conical pendulum of length $1\,m$ makes an angle $\theta \, = 45^o$ w.r.t. $Z-$ 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 $g\, = 10\, ms^{-2}$)
$0.4$
$4$
$0.2$
$2$
An aeroplane is flying with a uniform speed of $100\, m/s$ along a circular path of radius $100 m$. the angular speed of the aeroplane will be ......... $rad/sec$
Two racing cars of masses ${m_1}$ and ${m_2}$ are moving in circles of radii ${r_1}$ and ${r_2}$ respectively. Their speeds are such that each makes a complete circle in the same duration of time $t$. The ratio of the angular speed of the first to the second car is
A particle starting from rest, moves in a circle of radius $r$. It attains a velocity of $\mathrm{V}_{0} \;\mathrm{m} / \mathrm{s}$ in the $\mathrm{n}^{\text {th }}$ round. Its angular acceleration will be
A body is moving with constant speed, in a circle of radius $10 m$. The body completes one revolution in $4 s$. At the end of $3 rd$ second, the displacement of body (in $m$ ) from its starting point is:
The hour hand of a clock is $6\,cm$ long. The magnitude of the displacement of the tip of hour between $1:00\,PM$ to $5:00\,PM$ is