A ball of mass $1 \,kg$ is projected with a velocity of $20 \sqrt{2}\,m / s$ from the origin of an $x y$ co-ordinate axis system at an angle $45^{\circ}$ with $x$-axis (horizontal). The angular momentum [In $SI$ units] of the ball about the point of projection after $2 \,s$ of projection is [take $g=10 \,m / s ^2$ ] ( $y$-axis is taken as vertical)
A ball of mass $1 \,kg$ is projected with a velocity of $20 \sqrt{2}\,m / s$ from the origin of an $x y$ co-ordinate axis system at an angle $45^{\circ}$ with $x$-axis (horizontal). The angular momentum [In $SI$ units] of the ball about the point of projection after $2 \,s$ of projection is [take $g=10 \,m / s ^2$ ] ( $y$-axis is taken as vertical)
- A
$-400 \hat{k}$
- B
$200 \hat{i}$
- C
$300 \hat{j}$
- D
$-350 \hat{j}$
Similar Questions
A particle of mass $m$ is moving with constant velocity $v$ parallel to the $x$-axis as shown in the figure. Its angular momentum about origin $O$ is ..........
A particle of mass $m$ is moving with constant velocity $v$ parallel to the $x$-axis as shown in the figure. Its angular momentum about origin $O$ is ..........
Two thin circular discs of mass $m$ and $4 m$, having radii of $a$ and $2 a$, respectively, are rigidly fixed by a massless, rigid rod of length $l=\sqrt{24} a$ through their centers. This assembly is laid on a firm and flat surface, and set rolling without slipping on the surface so that the angular speed about the axis of the rod is $\omega$. The angular momentum of the entire assembly about the point ' $O$ ' is $\vec{L}$ (see the figure). Which of the following statement($s$) is(are) true?
($A$) The center of mass of the assembly rotates about the $z$-axis with an angular speed of $\omega / 5$
($B$) The magnitude of angular momentum of center of mass of the assembly about the point $O$ is $81 m a^2 \omega$
($C$) The magnitude of angular momentum of the assembly about its center of mass is $17 \mathrm{ma}^2 \mathrm{\omega} / 2$
($D$) The magnitude of the $z$-component of $\vec{L}$ is $55 \mathrm{ma}^2 \omega$
Two thin circular discs of mass $m$ and $4 m$, having radii of $a$ and $2 a$, respectively, are rigidly fixed by a massless, rigid rod of length $l=\sqrt{24} a$ through their centers. This assembly is laid on a firm and flat surface, and set rolling without slipping on the surface so that the angular speed about the axis of the rod is $\omega$. The angular momentum of the entire assembly about the point ' $O$ ' is $\vec{L}$ (see the figure). Which of the following statement($s$) is(are) true?
($A$) The center of mass of the assembly rotates about the $z$-axis with an angular speed of $\omega / 5$
($B$) The magnitude of angular momentum of center of mass of the assembly about the point $O$ is $81 m a^2 \omega$
($C$) The magnitude of angular momentum of the assembly about its center of mass is $17 \mathrm{ma}^2 \mathrm{\omega} / 2$
($D$) The magnitude of the $z$-component of $\vec{L}$ is $55 \mathrm{ma}^2 \omega$
- [IIT 2016]
A metre stick is pivoted about its centre. A piece of wax of mass $20 \,g$ travelling horizontally and perpendicular to it at $5 \,m / s$ strikes and adheres to one end of the stick so that the stick starts to rotate in a horizontal circle. Given the moment of inertia of the stick and wax about the pivot is $0.02 \,kg m ^2$, the initial angular velocity of the stick is ........... $rad / s$
A metre stick is pivoted about its centre. A piece of wax of mass $20 \,g$ travelling horizontally and perpendicular to it at $5 \,m / s$ strikes and adheres to one end of the stick so that the stick starts to rotate in a horizontal circle. Given the moment of inertia of the stick and wax about the pivot is $0.02 \,kg m ^2$, the initial angular velocity of the stick is ........... $rad / s$
Write the general formula of total angular moment of rotational motion about a fixed axis.
Write the general formula of total angular moment of rotational motion about a fixed axis.
Why $\vec v \times \vec p = 0$ for rotating particle ?
Why $\vec v \times \vec p = 0$ for rotating particle ?