(B) Let the mass of each sphere be $m$. The distance of $Q$ from $O$ is $r_Q = OP + PQ = 1\, m + 1\, m = 2\, m$. The distance of $P$ from $O$ is $r_P

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(B) Let the mass of each sphere be $m$. The distance of $Q$ from $O$ is $r_Q = OP + PQ = 1\, m + 1\, m = 2\, m$. The distance of $P$ from $O$ is $r_P = OP = 1\, m$.The tension $T_1$ in the string between $P$ and $Q$ provides the centripetal force for sphere $Q$:$T_1 = m r_Q \omega^2 = m(2)\omega^2 = 2m\omega^2$.The tension $T_2$ in the string between $O$ and $P$ must provide the centripetal force for both spheres $P$ and $Q$:$T_2 = m r_P \omega^2 + T_1 = m(1)\omega^2 + 2m\omega^2 = 3m\omega^2$.The ratio of the tensions is:$\frac{T_1}{T_2} = \frac{2m\omega^2}{3m\omega^2} = \frac{2}{3}$.

Class 11 Physics Newton's Laws of Motion and Friction Motion of Body (or Connected Bodies in horizontal or vertical) (by String or Contact)

Difficult

Two spheres $P$ and $Q$ of equal masses $m$ are attached to a string of total length $2\, m$ as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular velocity $\omega$. The distance $OP = 1\, m$ and $PQ = 1\, m$. What is the value of the ratio $\left( \frac{\text{Tension in the string between } P \text{ and } Q}{\text{Tension in the string between } O \text{ and } P} \right)?$

A
$1/2$
B
$2/3$
C
$3/2$
D
$2$

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Class 11

Physics Questions

Chapter

Newton's Laws of Motion and Friction

Subtopic

Motion of Body (or Connected Bodies in horizontal or vertical) (by String or Contact)

An elevator of mass $500 \,kg$ is ascending upwards with a constant acceleration $a=2 \,m/s^2$. What is the work done by the tension in the elevator cable during its climb by $12 \,m$ (in $\,kJ$)? (Take $g=10 \,m/s^2$)

EasyTS EAMCET 2020

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Three blocks of masses $4 \ kg$, $2 \ kg$, and $1 \ kg$ respectively are in contact on a frictionless table as shown in the figure. If a force of $14 \ N$ is applied on the $4 \ kg$ block, the contact force between the $4 \ kg$ and the $2 \ kg$ block will be: (in $N$)

MediumWBJEE 2012

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Two spheres $P$ and $Q$,each of mass $200 \text{ g}$,are attached to a string of length $1 \text{ m}$ as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that between $P$ and $O$ is (where $P$ is at the mid-point of the line joining $O$ and $Q$).

DifficultAP EAMCET 2018

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$A$ chain is lying on an absolutely smooth table,with half of it hanging over the edge of the table as shown in figure $(a)$. The time it takes to slip off the table is affected if two equal weights are attached,one to each end as shown in figure $(b)$.
$t_a$ : time taken to slip in situation $(a)$
$t_b$ : time taken to slip in situation $(b)$

Medium

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Two blocks of $7\,kg$ and $5\,kg$ are connected by a heavy rope of mass $4\,kg$. An upward force of $200\,N$ is applied as shown in the diagram. The tension at the top of the heavy rope at point $P$ is ....... $N$ $(g = 10\,m/s^2)$.

Difficult

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An elevator of mass $500 \,kg$ is ascending upwards with a constant acceleration $a=2 \,m/s^2$. What is the work done by the tension in the elevator cable during its climb by $12 \,m$ (in $\,kJ$)? (Take $g=10 \,m/s^2$)

Three blocks of masses $4 \ kg$, $2 \ kg$, and $1 \ kg$ respectively are in contact on a frictionless table as shown in the figure. If a force of $14 \ N$ is applied on the $4 \ kg$ block, the contact force between the $4 \ kg$ and the $2 \ kg$ block will be: (in $N$)

Two blocks of $7\,kg$ and $5\,kg$ are connected by a heavy rope of mass $4\,kg$. An upward force of $200\,N$ is applied as shown in the diagram. The tension at the top of the heavy rope at point $P$ is ....... $N$ $(g = 10\,m/s^2)$.

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