Two spheres $P$ and $Q$ of equal masses are attached to a string of length $2\,\, m$ as shown in figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant rate. What is the value of the ratio
$\left( {\frac{{{\text{Tension in the string between P and Q}}}}{{{\text{Tension in the string between P and O}}}}} \right)?$
$1/2$
$2/3$
$3/2$
$2$
A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of $0.5 \,m/s$. What is the height of the plane of circle from vertex of the funnel ........ $cm$
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 | $(s)$ $4 \sin 2$ |
A cyclist is riding with a speed of $27 \;km/h.$ As he approaches a circular turn on the road of radius $80\; m$, he applies brakes and reduces his speed at the constant rate of $0.50\; m/s$ every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn ?
A particle is tied to $20\, cm$ long string. It performs circular motion in vertical plane. What is the angular velocity of string when the tension in the string at the top is zero ........ $rad/sec$
A horizontal curve on $a$ racing track is banked at a $45^o $ angle. When a vehicle goes around this curve at the curve’s safe speed (no friction needed to stay on the track), what is its centripetal acceleration?