A particle of mass m is constrained to move o | vedclass

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

Question

(A) The particle moves under a constant force $F$ directed towards the equilibrium position $E$. This is a case of constant acceleration motion,not si

Vedclass · Accepted Answer

$4\sqrt{\frac{2Am}{F}}$

Vedclass · Answer

(A) The particle moves under a constant force $F$ directed towards the equilibrium position $E$. This is a case of constant acceleration motion,not simple harmonic motion.When the particle is at a distance $A$ from $E$,its acceleration is $a = \frac{F}{m}$.The time taken to reach $E$ from the starting position is calculated using the kinematic equation $s = ut + \frac{1}{2}at^2$. Here,$s = A$,$u = 0$,and $a = \frac{F}{m}$.$A = 0 + \frac{1}{2} \left(\frac{F}{m}ight) t_1^2 \implies t_1^2 = \frac{2Am}{F} \implies t_1 = \sqrt{\frac{2Am}{F}}$.This is the time taken to travel from the extreme position to the equilibrium position $E$. Due to symmetry,the particle will travel the same distance $A$ on the other side of $E$ and return to $E$ in the same time $t_1$,and then return to the starting position in another $2t_1$.The total time period $T$ is $4 	imes t_1 = 4\sqrt{\frac{2Am}{F}}$.

Similar Questions

Tripling the speed of the motor car multiplies the distance needed for stopping it by

The displacement of a particle is given by $y = a + bt + ct^2 - dt^4$. The initial velocity and acceleration are respectively

$A$ particle is moving with speed $v = b\sqrt{x}$ along the positive $x$-axis. Calculate the speed of the particle at time $t = \tau$ (assume that the particle is at the origin at $t = 0$).

$A$ particle moving along the $X$-axis has acceleration $f$ at time $t$ given by $f=f_0\left(1-\frac{t}{T}\right)$,where $f_0$ and $T$ are constants. The particle at $t=0$ has zero velocity. In the time interval between $t=0$ and the instant when $f=0$,the particle's velocity is

$A$ $100\, m$ long train is moving with a uniform velocity of $45\, km/hr$. The time taken by the train to cross a bridge of length $1\, km$ is.........$s$

Vedclass Test Series

Exam Paper Generator

Online Exam Module