Two objects A and B,each of mass m,are connec | vedclass

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

Question

(D) Let the acceleration of the system be $a$ along the ring. Since the string is inextensible,both objects $A$ and $B$ will have the same magnitude o

Vedclass · Accepted Answer

$mg/2$

Vedclass · Answer

(D) Let the acceleration of the system be $a$ along the ring. Since the string is inextensible,both objects $A$ and $B$ will have the same magnitude of acceleration $a$ along the tangent to the ring at their respective positions.For object $A$,the component of tension $T$ along the tangent is $T \cos(45^{\circ}) = T/\sqrt{2}$. Thus,the equation of motion for $A$ is:$T/\sqrt{2} = ma$ ......$(1)$For object $B$,the forces acting along the tangent are gravity $mg$ (acting downwards) and tension $T$ (acting upwards along the string). The component of gravity along the tangent is $mg \cos(45^{\circ}) = mg/\sqrt{2}$. The equation of motion for $B$ is:$mg/\sqrt{2} - T/\sqrt{2} = ma$ ......$(2)$Substituting $ma = T/\sqrt{2}$ from $(1)$ into $(2)$:$mg/\sqrt{2} - T/\sqrt{2} = T/\sqrt{2}$$mg/\sqrt{2} = 2T/\sqrt{2}$$T = mg/2$

Similar Questions

$A$ block of mass $48 \ kg$ kept on a smooth horizontal surface is pulled by a rope of length $4 \ m$ by a horizontal force of $25 \ N$ applied to the other end. If the linear density of the rope is $0.5 \ kg \ m^{-1}$,the force acting on the block is (in $N$)

The maximum tension a rope can withstand is $60 \,kg$-wt. The ratio of maximum acceleration with which two boys of masses $20 \,kg$ and $30 \,kg$ can climb up the rope at the same time is

$A$ block $P$ of mass $M_P$ is in contact with another block $Q$ of mass $M_Q$ as shown in the figure and they are placed on a smooth floor. Find the force on block $Q$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module