Two particles of mass m each are fixed at opposite ends of a massless rod of length 5m which is orie

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6.System of Particles and Rotational Motion

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Two particles of mass $m$ each are fixed at the opposite ends of a massless rod of length $5m$ which is oriented vertically on a smooth horizontal surface and released. Find the displacement of the lower mass on the ground when the rod makes an angle of $37^o$ with the vertical. ........ $m$

$1.5$

$2$

$2.5$

$3.5$

Solution

The rod is not pinned on the vertical in a point about it rotates and thus because of the symmetry of the system (equal masses at both ends) it needs to rotate about a point situated half the distance from each end. It is just like when you set loose the rod in middle air. Because of the symmetry it has, it will start rotating about its middle point (half distance from each end). See the figure below.

Therefore as can be seen from the figure the displacement on the horizontal of the lower mass is

$x=\left(\frac{l}{2}\right) \cdot \cos (37)=2.5 \cdot \sin (37)=1.5 m$

Standard 11

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hard

Two particles of mass $m$ each are fixed at the opposite ends of a massless rod of length $5m$ which is oriented vertically on a smooth horizontal surface and released. Find the displacement of the lower mass on the ground when the rod makes an angle of $37^o$ with the vertical. ........ $m$

Solution

Similar Questions

$A V$-shaped rigid body has two identical uniform arms. What must be the angle between the two arms, so that when the body is hung from one end the other arm is horizontal?

The left end of a massless stick with length $l$ is placed on the corner of a table, as shown in Fig. A point mass $m$ is attached to the center of the stick, which is initially held horizontal. It is then released. Immediately afterward, what normal force does the table exert on the stick?

In an experiment with a beam balance on unknown mass $m$ is balanced by two known mass $m$ is balanced by two known masses of $16\, kg$ and $4\, kg$ as shown in figure. The value of the unknown mass $m$ is ……. $kg$.

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