A wire is bent into the shape of a parabola g | vedclass

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

Question

(B) When the bead is in equilibrium relative to the wire,the forces acting on it in the frame of the wire are gravity ($mg$ downwards),pseudo force ($

Vedclass · Accepted Answer

$\frac{a}{2gk}$

Vedclass · Answer

(B) When the bead is in equilibrium relative to the wire,the forces acting on it in the frame of the wire are gravity ($mg$ downwards),pseudo force ($ma$ in the negative $X$-direction),and the normal force $(N)$.At equilibrium,the net force along the wire is zero.Resolving forces: $N \cos 	heta = mg$ and $N \sin 	heta = ma$,where $	heta$ is the angle the tangent makes with the horizontal.Dividing the two equations,we get $	an 	heta = \frac{a}{g}$.The slope of the parabola $Y = Kx^2$ is given by $\frac{dy}{dx} = 2Kx$.Since the slope is equal to $	an 	heta$,we have $2Kx = \frac{a}{g}$.Solving for $x$,we get $x = \frac{a}{2Kg}$.

Similar Questions

$A$ spring balance is attached to the ceiling of a lift. $A$ man hangs his bag on the spring and the spring balance reads $49 \,N$, when the lift is stationary. If the lift moves downward with an acceleration of $5 \,m/s^2$, the reading of the spring balance will be $(g = 9.8 \,m/s^2)$. (in $\,N$)

$A$ coin is dropped in a lift. It takes time $t_1$ to reach the floor when the lift is stationary. It takes time $t_2$ when the lift is moving up with constant acceleration $a$. Then:

$A$ simple pendulum is set up in a trolley which moves to the right with an acceleration $a$ on a horizontal plane. Then the thread of the pendulum in the mean position makes an angle $\theta$ with the vertical.

$A$ child stands on a weighing machine inside a lift. When the lift is going down with acceleration $\frac{g}{3}$,the machine shows a reading $20 \ N$. When the lift goes upwards with acceleration $\frac{g}{3}$,the reading would be ($g=$ gravitational acceleration). (in $N$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module