A particle moves in a circular path with decreasing speed. Choose the correct statement.
Angular momentum remains constant
Acceleration ($\vec a$) is towards the center
Particle moves in a spiral path with decreasing radius
The direction of angular momentum remains constant
$Assertion$ : When a particle moves in a circle with a uniform speed, its velocity and acceleration both changes.
$Reason$ : The centripetal acceleration in circular motion is dependent on angular velocity of the body.
For circular motion, if ${\vec a_t},\,{\vec a_c},\,\vec r$ and $\vec v$ are tangential acceleration, centripetal acceleration, radius vector and velocitym respectively, then find the wrong relation
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 simple pendulum consisting of a mass $M$ attached to a string of length $L$ is released from rest at an angle $\alpha$. $A$ pin is located at a distance $l$ below the pivot point. When the pendulum swings down, the string hits the pin as shown in the figure. The maximum angle $\theta$ which string makes with the vertical after hitting the pin is :-
A missile is fired for maximum range at your town from a place $100\, km$ away from you. If the missile is first detected at its half way point, how much warning time will you have ? (Take $g = 10\, m/s^2$) what was the speed of missile when it was detected ?