See Figure given below. A mass of $6 \;kg$ is suspended by a rope of length $2 \;m$ from the ceiling. A force of $50\; N$ in the horizontal direction is applied at the midpoint $P$ of the rope, as shown. What is the angle the rope makes with the vertical in equilibrium ? (Take $g = 10 \;m s^{-2}$). Neglect the mass of the rope.
See Figure given below. A mass of $6 \;kg$ is suspended by a rope of length $2 \;m$ from the ceiling. A force of $50\; N$ in the horizontal direction is applied at the midpoint $P$ of the rope, as shown. What is the angle the rope makes with the vertical in equilibrium ? (Take $g = 10 \;m s^{-2}$). Neglect the mass of the rope.
Consider the equilibrium of the weight $W$
$\text { Clearly, } T_{2}=6 \times 10=60 \,N$
Consider the equilibrium of the point P under the action of three forces - the tensions $T_{1}$ and $T_{2},$ and the horizontal force $50 N$. The horizontal and vertical components of the resultant force must vanish separately
$T_{1} \cos \theta=T_{2}=60 \,N$
$T_{1} \sin \theta=50 \,N$which gives that
$\tan \theta=\frac{5}{6} \text { or } \theta=\tan ^{-1}\left(\frac{5}{6}\right)=40^{\circ}$
Similar Questions
A particle of mass $m$ is constrained to move on $x$-axis. A force $F$ acts on the particle. $F$ always points toward the position labeled E. For example, when the particle is to the left of $E$, $F$ points to the right. The magnitude of $F$ is constant except at point $E$ where it is zero.
The system is horizontal. $F$ is the net force acting on the particle. The particle is displaced a distance A towards left from the equilibrium position $E$ and released from rest at $t=0$
Velocity-time graph of the particle is
The system is horizontal. $F$ is the net force acting on the particle. The particle is displaced a distance A towards left from the equilibrium position $E$ and released from rest at $t=0$
Velocity-time graph of the particle is
Which of the following sets of concurrent forces may be in equilibrium
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Consider a frame that is made up of two thin massless rods $AB$ and $AC$ as shown in the figure. $A$ vertical force $\overrightarrow{ P }$ of magnitude $100 \;N$ is applied at point $A$ of the frame. Suppose the force is $\overrightarrow{ P }$ resolved parallel to the arms $AB$ and $AC$ of the frame. The magnitude of the resolved component along the arm $AC$ is $xN$. The value of $x$, to the nearest integer, is ............
[Given : $\sin \left(35^{\circ}\right)=0.573, \cos \left(35^{\circ}\right)=0.819$ $\left.\sin \left(110^{\circ}\right)=0.939, \cos \left(110^{\circ}\right)=-0.342\right]$
Consider a frame that is made up of two thin massless rods $AB$ and $AC$ as shown in the figure. $A$ vertical force $\overrightarrow{ P }$ of magnitude $100 \;N$ is applied at point $A$ of the frame. Suppose the force is $\overrightarrow{ P }$ resolved parallel to the arms $AB$ and $AC$ of the frame. The magnitude of the resolved component along the arm $AC$ is $xN$. The value of $x$, to the nearest integer, is ............
[Given : $\sin \left(35^{\circ}\right)=0.573, \cos \left(35^{\circ}\right)=0.819$ $\left.\sin \left(110^{\circ}\right)=0.939, \cos \left(110^{\circ}\right)=-0.342\right]$
- [JEE MAIN 2021]
In the system shown in the adjoining figure, the tension $T_2$ is
In the system shown in the adjoining figure, the tension $T_2$ is
A dynamometer $D$ is attached to two blocks of masses $6 \,kg$ and $4 \,kg$ as shown in the figure. The reading of the dynamometer is ............ $N$
A dynamometer $D$ is attached to two blocks of masses $6 \,kg$ and $4 \,kg$ as shown in the figure. The reading of the dynamometer is ............ $N$