Objects A and B,each of mass m,are connected | vedclass

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

Question

(A) Let the tension in the cord be $T$. At the instant of release,the objects $A$ and $B$ are at rest,so their acceleration is zero. For object $A$,th

Vedclass · Accepted Answer

$\frac{mg}{\sqrt{2}}$

Vedclass · Answer

(A) Let the tension in the cord be $T$. At the instant of release,the objects $A$ and $B$ are at rest,so their acceleration is zero. For object $A$,the forces acting are gravity ($mg$ downwards) and tension ($T$ along the cord). The component of gravity along the cord is $mg \cos 45^{\circ}$. Since the object is constrained to move on the ring,the net force along the tangent to the ring must be considered. For object $A$,the component of gravity along the tangent is $mg \sin 45^{\circ}$. For object $B$,the component of gravity along the tangent is $mg \cos 45^{\circ}$. Since the cord is inextensible,both objects must have the same acceleration $a$ along the tangent. For $A$: $mg \sin 45^{\circ} - T = ma$ For $B$: $T - mg \cos 45^{\circ} = ma$ Adding the two equations: $mg(\sin 45^{\circ} - \cos 45^{\circ}) = 2ma$. Since $\sin 45^{\circ} = \cos 45^{\circ}$,$a = 0$. Substituting $a=0$ into the second equation: $T = mg \cos 45^{\circ} = \frac{mg}{\sqrt{2}}$.

Objects $A$ and $B$,each of mass $m$,are connected by a light inextensible cord. They are constrained to move on a frictionless ring in a vertical plane as shown in the figure. The objects are released from rest at the positions shown. The tension in the cord just after release will be

Similar Questions

Two blocks of masses $m$ and $M$ are connected by means of a metal wire of cross-sectional area $A$ passing over a frictionless fixed pulley as shown in the figure. The system is then released. If $M = 2m$,then the stress produced in the wire is

$A$ smooth massless string passes over a smooth fixed pulley. Two masses $m_{1}$ and $m_{2}$ $(m_{1} > m_{2})$ are tied at the two ends of the string. The masses are allowed to move under gravity starting from rest. The total external force acting on the two masses is

In the system shown in the figure,the pulleys and strings are ideal. Find the acceleration of $m_1$ with respect to $m_2$ $(m_1 = 2\ kg, m_2 = 2\ kg)$.

If $m_1 = 4m_2$ and the acceleration of $m_1$ is $a$,find the tension $T$ in the string.

Vedclass Test Series

Exam Paper Generator

Online Exam Module