If a trolley accelerates horizontally with ac | vedclass

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

Question

(D) In the frame of reference of the trolley,a pseudo force $F_p = ma$ acts on the bob in the direction opposite to the acceleration of the trolley.Le

Vedclass · Accepted Answer

$	heta=	an ^{-1}\left(\frac{a}{g}ight)$

Vedclass · Answer

(D) In the frame of reference of the trolley,a pseudo force $F_p = ma$ acts on the bob in the direction opposite to the acceleration of the trolley.Let $m$ be the mass of the bob,$T$ be the tension in the string,and $	heta$ be the angle of deflection from the vertical.In equilibrium,the forces acting on the bob are:$1$. Tension $T$ along the string.$2$. Gravitational force $mg$ acting vertically downwards.$3$. Pseudo force $ma$ acting horizontally backwards.Resolving the forces along the direction of the string and perpendicular to it:Along the string: $T = mg \cos 	heta + ma \sin 	heta$Perpendicular to the string: $T \sin 	heta = ma \cos 	heta$ (This is not the standard way,let's use horizontal and vertical components).Alternatively,balancing forces in the horizontal and vertical directions:Horizontal: $T \sin 	heta = ma$Vertical: $T \cos 	heta = mg$Dividing the two equations:$\frac{T \sin 	heta}{T \cos 	heta} = \frac{ma}{mg}$$	an 	heta = \frac{a}{g}$$	heta = 	an ^{-1}\left(\frac{a}{g}ight)$

If a trolley accelerates horizontally with acceleration $a$,then the bob is displaced backward from its initial vertical position. The angular deflection of the bob in equilibrium is ..........

Similar Questions

In an elevator moving vertically up with an acceleration $g$,the force exerted on the floor by a passenger of mass $M$ is

$A$ person standing on a spring balance inside a stationary lift measures $60 \, kg$. The weight of that person if the lift descends with a uniform downward acceleration of $1.8 \, m/s^{2}$ will be $_{-} N$. $[g = 10 \, m/s^{2}]$

Two bodies of masses $m_1$ and $m_2$ are connected by a light string which passes over a frictionless,massless pulley. If the pulley is moving upward with uniform acceleration $\frac{g}{2}$,then the tension in the string will be .........

$A$ car is moving on a circular horizontal track of radius $10 \, m$ with a constant speed of $10 \, m/s$. $A$ plumb bob is suspended from the roof of the car by a light rigid rod of length $1.00 \, m$. The angle made by the rod with the vertical is ........ $^o$.

$A$ block of mass $m$ is placed on a smooth wedge of inclination $\theta$. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block ($g$ is acceleration due to gravity) will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module