A conical pendulum is moving in a circle with angular velocity $\omega $ as shown. If tension in the string is $T$ , which of following equation are correct?
$T = m{\omega ^2}l$
$T\,\sin \,\theta = m{\omega ^2}l$
$T = mg\,\cos \theta $
$T\, = m{\omega ^2}\,l\,\sin \,\theta $
$Assertion$ : Centripetal and centrifugal forces cancel each other.
$Reason$ : Centrifugal force is a reaction of centripetal force
A particle is rotating in a circle of radius $1\,m$ with constant speed $4\,m / s$. In time $1\,s$, match the following (in $SI$ units) columns.
Colum $I$ | Colum $II$ |
$(A)$ Displacement | $(p)$ $8 \sin 2$ |
$(B)$ Distance | $(q)$ $4$ |
$(C)$ Average velocity | $(r)$ $2 \sin 2$ |
$(D)$ Average acceleration | $(s)$ $4 \sin 2$ |
Three point particles $P, Q, R$ move in circle of radius $‘r’$ with different but constant speeds. They start moving at $t = 0$ from their initial positions as shown in the figure. The angular velocities (in rad/ sec) of $P, Q$ and $R$ are $5\pi , 2\pi$ & $3\pi$ respectively, in the same sense. the number of times $P$ and $Q$ meet in that time interval is:
A clock has $75 \mathrm{~cm}, 60 \mathrm{~cm}$ long second hand and minute hand respectively. In $30$ minutes duration the tip of second hand will travel $x$ distance more than the tip of minute hand. The value of $x$ in meter is nearly (Take $\pi=3.14$ ) :
A car changes speed from $18\,km/h$ to $36\,km/h$ in $5\,s$. The diameter of its wheel is $0.8\,m$ . The angular acceleration of the wheel is ........ $rad/s^2$