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 | $(s)$ $4 \sin 2$ |
$( A \rightarrow r , B \rightarrow q , C \rightarrow r , D \rightarrow p )$
$( A \rightarrow p , B \rightarrow q , C \rightarrow r , D \rightarrow p )$
$( A \rightarrow r , B \rightarrow s , C \rightarrow r , D \rightarrow p )$
$( A \rightarrow p , B \rightarrow q , C \rightarrow r , D \rightarrow s)$
Which of the following quantities remains constant during uniform circular motion?
A motor cyclist going round in a circular track at constant speed has
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?
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
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
$\left( {\frac{{{\text{Tension in the string between P and Q}}}}{{{\text{Tension in the string between P and O}}}}} \right)?$