A particle moves in a plane along an elliptic | vedclass

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

Question

(A) The path of the particle is given by $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$.Differentiating with respect to time $t$,we get $\frac{2x}{a^2} \frac

Vedclass · Accepted Answer

$-b u^2 / a^2$

Vedclass · Answer

(A) The path of the particle is given by $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$.Differentiating with respect to time $t$,we get $\frac{2x}{a^2} \frac{dx}{dt} + \frac{2y}{b^2} \frac{dy}{dt} = 0$,which simplifies to $\frac{x}{a^2} v_x + \frac{y}{b^2} v_y = 0 \dots (i)$.Differentiating again with respect to time $t$,we get $\frac{1}{a^2} (v_x^2 + x a_x) + \frac{1}{b^2} (v_y^2 + y a_y) = 0 \dots (ii)$.At point $(0, b)$,we have $x = 0$ and $y = b$. Given $v_x = u$ at this point.Substituting $x = 0$ into equation $(i)$,we get $\frac{0}{a^2} u + \frac{b}{b^2} v_y = 0$,which implies $v_y = 0$.Now,substituting $x = 0, y = b, v_x = u, v_y = 0$ into equation $(ii)$,we get $\frac{1}{a^2} (u^2 + 0 \cdot a_x) + \frac{1}{b^2} (0^2 + b \cdot a_y) = 0$.This simplifies to $\frac{u^2}{a^2} + \frac{b a_y}{b^2} = 0$,or $\frac{u^2}{a^2} + \frac{a_y}{b} = 0$.Therefore,$a_y = -\frac{b u^2}{a^2}$.

$A$ particle moves in a plane along an elliptic path given by $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. At point $(0, b)$,the $x$-component of velocity is $u$. The $y$-component of acceleration at this point is

Similar Questions

$A$ sportsman runs around a circular track of radius $r$ such that he traverses the path $ABAB$. The distance travelled and displacement,respectively,are

$A$ projectile crosses two walls of equal height $H$ symmetrically as shown. The height of each wall is ........ $m$.

$A$ particle of mass $m$ performs uniform circular motion of radius $r$ with linear speed $v$ under the application of force $F$. If $m, v$ and $r$ are all increased by $50 \%$,the necessary change in force required to maintain the particle in uniform circular motion is (in $\%$)

$A$ boy throws a cricket ball from the boundary to the wicket-keeper. If the frictional force due to air cannot be ignored,the forces acting on the ball at the position $X$ are represented by

$A$ small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track,the normal reaction is maximum in

Vedclass Test Series

Exam Paper Generator

Online Exam Module