A particle moves in a circular path of radius $r$ with speed $v.$ It then increases its speed to $2\,v$ while travelling along the same circular path. The centripetal acceleration of the particle has changed by a factor of
$0.25$
$0.5$
$2$
$4$
$(a)$ Earth can be thought of as a sphere of radius $6400\, km$. Any object (or a person) is performing circular motion around the axis of the earth due to the earth rotation (period $1$ day). What is acceleration of object on the surface of the earth (at equator) towards its centre ? What is it at latitude $(\theta )$ ? How does these accelerations compare with $g=9.8\,m/s^2$ ?
$(b)$ Earth also moves in circular orbit around the sun once every year with an orbital radius of $1.5 \times 10^{11} \,m$. What is the acceleration of the earth (or any object on the surface of the earth) towards the centre of the sun ? How does this acceleration compare with $g=9.8\,m/s^2$ ?
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
A stone ties to the end of a string $1\,m$ long is whirled in a horizontal circle with a constant speed. If the stone makes $22$ revolution in $44$ seconds, what is the magnitude and direction of acceleration of the stone
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 ........ $rad/s^2$
An aircraft executes a horizontal loop of radius $1.00\; km$ with a steady speed of $900 \;km/h$. Compare its centripetal acceleration with the acceleration due to gravity.