Motion In Two Dimensions

A disc of radius $2 \mathrm{~m}$ is rotating with angular is to be put on the disc. Friction coefficient between disc and block is $\mu_{\mathrm{K}}=0.3$, then find the maximum distance from axis where the block can be…

A projectile has a maximum range of $16 \mathrm{~km}$. At the highest point of its motion, it explodes into two equal masses. One mass drops vertically downwards. The horizontal distance covered by the other mass from…

A particle is moving with a constant speed $v$ in a circle. What is the magnitude of average velocity after half rotation?

Assertion : For angular projection, when angle of projection $\theta=\tan ^{-1}(1)$, the horizontal range is four times the maximum height. Reason : The horizontal range of projectile is directly proportional to square…

Assertion : For a projectile the time of flight of a body becomes $n$ times the original value if its speed is made $n$ times. Reason : This is due to the range of the projectile which becomes $n$ times.

A particle is projected from the ground with an initial speed of $v$ at an angle $\theta$ with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is

A projectile is given an initial velocity of $\hat{i}+2 \hat{j}$. The cartesian equation of its path is (Take $g=10 \mathrm{~m} \mathrm{~s}^{-2}$)

A wheel starts rotating from rest at time $t=0$ with a angular acceleration of 50 radians $/ \mathrm{s}^2$. The angular acceleration $(\alpha)$ decreases to zero value after 5 seconds. During this interval, $\alpha$…

A string $0.5 \mathrm{~m}$ long is used to whirl a $1 \mathrm{~kg}$ stone in a vertical circle at a uniform velocity of $5 \mathrm{~m} \mathrm{~s}^{-1}$. What is the tension in the string when the stone is at the top of…

The radii of circular paths of two particles of same mass are in ratio $6: 8$ then what will be velocities ratio if they have a constant centripetal force?

An arrow is projected into air. Its time of flight is $5 \mathrm{~s}$ and range $200 \mathrm{~m}$. What is the maximum height reached by it? (Take $g=10 \mathrm{~m} \mathrm{~s}^{-2}$)

A ball of mass $m$ is tied up with string and rotated along a horizontal circle of radius $r$. At an instant, its velocity is $v$, and tension in string is $T$, the force required for circular motion is