A smooth sphere is moving on a horizontal sur | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The initial velocity of the sphere is $\vec{u} = 2 \hat{i} + 2 \hat{j} \ m/s$.Since the wall is parallel to the $y$-axis (vector $\hat{j}$),the wa

Vedclass · Accepted Answer

$-\hat{i} + 2 \hat{j}$

Vedclass · Answer

(B) The initial velocity of the sphere is $\vec{u} = 2 \hat{i} + 2 \hat{j} \ m/s$.Since the wall is parallel to the $y$-axis (vector $\hat{j}$),the wall is perpendicular to the $x$-axis.During the collision,the impulse acts only along the normal to the wall,which is the $x$-direction.Therefore,the velocity component parallel to the wall ($y$-component) remains unchanged: $v_y = u_y = 2 \hat{j} \ m/s$.For the $x$-component,we use the coefficient of restitution $e = -\frac{v_x}{u_x}$,where $u_x = 2 \ m/s$ and $e = 1/2$.$v_x = -e \cdot u_x = -\frac{1}{2} \cdot 2 = -1 \ m/s$.Thus,the velocity vector after the collision is $\vec{v} = v_x \hat{i} + v_y \hat{j} = -1 \hat{i} + 2 \hat{j} \ m/s$.

Similar Questions

$A$ tennis ball is released from height $h$ above ground level. If the ball makes an inelastic collision with the ground,to what height will it rise after the third collision?

$A$ ball of mass $m$ moving with velocity $v$ collides head-on with a second ball of mass $m$ at rest. If the coefficient of restitution is $e$,the velocity of the first ball after collision is $v_1$,and the velocity of the second ball after collision is $v_2$,then:

$A$ body of mass $m_1$ moving with a velocity $3 \, ms^{-1}$ collides with another body at rest of mass $m_2$. After the collision,the velocities of the two bodies are $2 \, ms^{-1}$ and $5 \, ms^{-1}$ respectively along the direction of motion of $m_1$. The ratio $\frac{m_1}{m_2}$ is:

$A$ sphere of mass $m$ moving with velocity $v$ collides head-on with another sphere of the same mass which is at rest. The ratio of the final velocity of the second sphere to the initial velocity of the first sphere is (where $e$ is the coefficient of restitution and the collision is inelastic).

Vedclass Test Series

Exam Paper Generator

Online Exam Module