Tension in a String

Q. Find the ratio of tensions $T_1$ to $T_2$ for the figure shown.

1. $8:5$
2. $5:8$
3. $3:4$
4. $4:3$

Q. For the system shown in the figure, if $F_2$ and $F_3$ are forces acting on the masses $m_2$ and $m_3$ respectively, then the correct relation between the forces is (Assume that the blocks are connected by inextensible strings and the surface is frictionless)

1. $F_3=F_1+F_2$
2. $F_3=\frac{m_1{F}_1}{m_1+m_2+m_3}$
3. $F_3=\frac{m_2{F}_1}{m_1+m_2+m_3}$
4. $F_3=\frac{m_3{F}_1}{m_1+m_2+m_3}$

Q. In the following figure the masses of the blocks $A$ and $B$ are the same and each equal to $m$. The tensions in the strings $OA$ and $AB$ are $T_2$ and $T_1$ respectively. The system is in equilibrium with a constant horizontal force $mg$ on $B$. Then $T_2$ is:

1. $mg$
2. $\sqrt{2}mg$
3. $\sqrt{3}mg$
4. $\sqrt{5}mg$

Q.

Find the tension in the string and the acceleration of the blocks?

1. T = 3 N , a= 3m/$s^2$

2. T = 4 N , a= 4m/$s^2$

3. T = 6 N , a= 2m/$s^2$

4. None of these

Q. Find the acceleration of the system shown in the figure.

1. $\frac{g}{7}$
2. $\frac{g}{3}$
3. $\frac{2g}{5}$
4. $\frac{2g}{7}$

Q. Two blocks are connected with a string and the system is connected to another string which is fixed at the centre of a circular table as shown in the figure. The table is rotating with an angular speed of $\omega$ about its centre. Find the tension in the string which is fixed at the centre.

1. $m{\omega }^2{r}_1$
2. $m{\omega }^2{r}_2$
3. $m{\omega }^2(r_1+r_2)$
4. $m{\omega }^2(r_1-r_2)$

Q. In the figure the block of mass M is at rest on the floor. The acceleration with which a monkey of mass m should climb up along the rope of negligible mass so as to lift the block from the floor is,

1. $=(\frac{M}{m}-1)g$
2. > $(\frac{M}{m}-1)g$
3. $=\frac{M}{m}g$
4. > $\frac{M}{m}g$

Q. If $F=120N$ which is parallel to the inclined plane, find the tension $T_2$ in string. $(g=10m/s^2)$

1. $15N$
2. $30N$
3. $45N$
4. $60N$

Q. In the figure shown, the $12kg$ body pulled by a string with an acceleration $a=2.2m/s^2$. The tension $T_1$ and $T_2$ will be respectively
(Take $g=9.8m/s^2$)

1. $200N,80N$
2. $240N,90N$
3. $240N,96N$
4. $260N,96N$

Q. Three equal weights $A,B$ and $C$ of mass 2 kg each are hanging on a string passing over a fixed frictionless pulley as shown in the figure. The tension in the string connecting weights $B$ and $C$ is

1. Zero
2. $13\text{N}$
3. $3.3\text{N}$
4. $19.6\text{N}$

Q. A body of mass $5\text{kg}$ is suspended by the strings making angles ${60}^o$ and ${30}^o$ with the horizontal as shown in the figure. Find the tension in the strings. ($g=10{\text{m/s}}^2$ )

1. $T_1=25\text{N}$ & $T_2=25\text{N}$
2. $T_1=25\sqrt{3}\text{N}$ & $T_2=25\text{N}$
3. $T_1=25\text{N}$ & $T_2=25\sqrt{3}\text{N}$
4. $T_1=25\sqrt{3}\text{N}$ & $T_2=25\sqrt{3}\text{N}$

Q. Two blocks of masses $6kg$ and $4kg$ connected by a rope of mass $2kg$ are resting on a frictionless floor as shown in the figure. If a constant force $60N$ is applied to the $6kg$ block, find the tension in the rope at points $A,B$ and $C$. $B$ is at the mid-point and points $A$ and $C$ are at the ends. Assume that the mass of the rope is uniformly distributed along its length.

1. $30N,25N,20N$ respectively
2. $20N,20N,30N$ respectively
3. $30N,20N,25N$ respectively
4. None of the above

Q. Three blocks of mass $2kg$, $3kg$ and $5kg$ are connected to each other with light string and are then placed on a frictionless surface as shown in the figure. The system is pulled by a force of $10\text{N}$, tension $T_1$ is equal to

1. $1N$
2. $5N$
3. $8N$
4. $10N$

Q. In both the cases, block & monkey are at the same horizontal level. In both the cases, monkey climbs the rope. In case-1 rope remains vertical & in case-2 rope swings during motion. $t_1\&t_2$ are times taken by monkeys to reach the pulley in case-1 & case-2 respectively. In both cases, monkey applies the same force on the rope.

1. $t_1=t_2$
2. $t_1<t_2$
3. In case-2, block reaches the pulley earlier than monkey
4. In case-1, monkey reaches the pulley earlier than block

Q. In the figure shown, find the tension $T_1$ (in $N$) in the string. Assume the strings to be inextensible and pulley frictionless.

1. $2g$
2. $3g$
3. $2.5g$
4. $4g$

Q. Find $F$ such that the $2\text{kg}$ body goes up with an acceleration of $2{\text{m/s}}^2$.
Take ($g=10{\text{m/s}}^2$)

1. $10\text{N}$
2. $20\text{N}$
3. $25\text{N}$
4. $30\text{N}$

Q. A string of length $1\text{m}$ is fixed at one end and carries a mass of $100\text{g}$ at the other end. The string makes $\left(2/\pi \right)$ revolutions per second around vertical axis through the fixed end. What is the tension in the string :-

1. $1.6\text{N}$
2. $0.8\text{N}$
3. $3.2\text{N}$
4. $2.4\text{N}$

Q. A mass $m$ is suspended by a rope from a rigid support at P as shown in the figure. Another rope is tied at the end Q which is pulled horizontally with a force $F$. If the rope PQ makes angle $\theta$ with the vertical, then tension in the string PQ is

1. $F\sin \theta$
2. $\frac{F}{\sin \theta }$
3. $F\cos \theta$
4. $\frac{F}{\cos \theta }$

Q. In two pulley - particle figures (i) and (ii), the acceleration and force imparted by the string on the pulley and tension in the strings are, $(a_1,a_2),(N_1,N_2)$, and $(T_1,T_2)$ respectively. Ignoring friction in all contacting surfaces, which of the following relations is true?

1. $\frac{a_1}{a_2}=1$
2. $\frac{T_1}{T_2}<1$
3. $\frac{N_1}{N_2}>1$
4. $\frac{a_1}{a_2}<1$

Q. A steel ball is suspended from the ceiling of an accelerating carriage by means of two cords $\text{A}$ and $\text{B}$. Determine the acceleration $a$ ( in ${\text{m/s}}^2$) of the carriage which will cause the tension in A to be twice that in B

1. $g\sqrt{3}$
2. $\frac{g}{\sqrt{3}}$
3. $3\sqrt{3}g$
4. $\frac{g}{3\sqrt{3}}$

Q. A ball of mass $1\text{kg}$ hangs in equilibrium from two strings $OA$ and $OB$ as shown in the figure. What are the tensions in strings $OA$ and $OB$? (Take $g=10{\text{ms}}^{-2}$)

1. $5\text{N}$, zero
2. zero, $N$
3. $5\text{N},5\sqrt{3}\text{N}$
4. $5\sqrt{3}\text{N},5\text{N}$

Q. In the figure shown, all the blocks are of equal mass of $10\text{kg}$ and $F=300\text{N}$. Find the tension in the string, $T_{BC}$. Assume all surface to be smooth and $g=10{\text{m/s}}^2$.

1. $100\text{N}$
2. $150\text{N}$
3. $200\text{N}$
4. $250\text{N}$

Q. Two blocks of masses $m$ and $2m$ are placed on triangular wedge by means of a massless inextensible string over a frictionless fixed pulley. Surface of contact between the masses and wedge is frictionless and wedge makes ${45}^{\circ }$ with horizontal on both sides as shown in figure. The tensions in the string $\left(T\right)$ is

1. $\frac{4mg}{3\sqrt{2}}\text{N}$
2. $\frac{2mg}{3\sqrt{2}}\text{N}$
3. $\frac{mg}{3\sqrt{2}}\text{N}$
4. $\frac{3mg}{\sqrt{2}}\text{N}$

Q. Two beads A and B of equal mass $m$ are connected by a light rod, which acts as a chord for the ring. They are constrained to move on the frictionless ring in a vertical plane. The beads are released from rest as shown in figure. The tension in the chord just after release will be:

1. $\frac{mg}{4}$
   
2. $\sqrt{2}mg$
3. $\frac{mg}{2}$
   
4. $\frac{mg}{\sqrt{2}}$

Q. If force, $F=48N$ is acting on the system as shown in figure, find the tension in string. All surfaces are smooth.
(Take $g=10m/s^2$)

1. $12N$
2. $9.6N$
3. $8.4N$
4. $5.6N$

Q. Three blocks $A$, $B$ and $C$ weighing $1kg,8kg$ and $27kg$ respectively are connected as shown in the figure, with an inextensible string and are moving on a smooth surface. If tension $T_3$ is equal to $36N$, then tension $T_2$ is

1. $18N$
2. $9N$
3. $3.375N$
4. $1.25N$

Q. A particle is suspended by thread of length $l$ from a fixed point. If it is launched from the bottom with a horizontal speed of $v=\sqrt{5gl}$, then tension in the thread when the particle is at the topmost point

1. $T=mg$
2. $T=0$
3. $T=5mg$
4. $T=6mg$

Q. In the figure shown, all the blocks are of equal mass of $10\text{kg}$ and $F=300\text{N}$. Find the tension in the string $T_{AB}$. Assume all surface to be smooth and $g=10{\text{m/s}}^2$.

1. $100\text{N}$
2. $150\text{N}$
3. $200\text{N}$
4. $250\text{N}$

Q. Two containers of sand are arranged like the block as shown in figure. The containers alone have negligible mass; the sand in these containers has a total mass $M_{tot}$; the sand in the hanging container $H$ has mass $m$.
To measure the magnitude of the acceleration of the system, a large number of experiments have been carried out where $m$ varies from experiment to experiment but $M_{tot}$ does not; that is, sand is shifted between the containers before each trial.


Which of the curves gives the tension in the connecting cord (the vertical axis is for tension)?

1. $1$
2. $2$
3. $3$
4. $4$

Q. In the figure shown, find the tension in the string connecting the blocks of mass $2kg$ and $3kg$. Take $g=10m/s^2$

1. $10N$
2. $12.4N$
3. $13.6N$
4. $15.2N$