Tension in a String

Q. In Youngs double slit experiment, how many maximas can be obtained on a screen (including the central maximum) on both sides of the central fringe if $\lambda =2000$ Angstrom and $d=7000$ Angstrom

Q.

A pendulum bob of mass 80 mg and carrying a charge of $2\times {10}^{-8}C$ is at rest in a uniform horizontal electric field of $20kV{m}^{-1}$ Find the tension in the thread.

Q. Find the reading of the spring balance considering spring, pulley and string to be massless.

1. $600\text{N}$
2. $300\text{N}$
3. $400\text{N}$
4. $200\text{N}$

Q. Three blocks of masses $m_1$, $m_2$ and $m_3$ are connected by massless strings as shown in the figure and placed on a frictionless table. They are pulled with a force $T_3=40N$. The tension $T_2$ will be: (Given $m_1=10kg,m_2=6kg$ and $m_3=4kg$)

1. $20N$
2. $40N$
3. $10N$
4. $32N$

Q. A string of negligible mass going over a clamped pulley of mass $m$ supports a block of mass $M$ as shown in the figure. The force on the pulley by the clamp is

1. $\sqrt{2}Mg$
2. $\sqrt{2}mg$
3. $g\sqrt{(M-m{)}^2+m^2}$
4. $g\sqrt{(M+m{)}^2+M^2}$

Q. A pendulum bob of mass $40\text{mg}$ and carrying a charge of $2\times {10}^{-8}\text{C}$ is at rest in a horizontal uniform electric field of $2\times {10}^7{\text{Vm}}^{-1}$. Calculate the tension in the thread of the pendulum and the angle it makes with the vertical.

1. $\theta ={45}^{\circ },T=\sqrt{32}\times {10}^{-1}\text{N}$
2. $\theta ={45}^{\circ },T=\sqrt{8}\times {10}^{-1}\text{N}$
3. $\theta ={30}^{\circ },T=\sqrt{32}\times {10}^{-1}\text{N}$
4. $\theta ={30}^{\circ },T=\sqrt{8}\times {10}^{-1}\text{N}$

Q. A block of mass $10kg$ is suspended by three strings as shown in the figure. The tension $T_2$ is (Take $g=10m/s^2$)

1. $100N$
2. $100\sqrt{3}N$
3. $50\sqrt{3}N$
4. $\frac{100}{\sqrt{3}}N$

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

Q. Two bodies of mass 4 kg and 6 kg are attached to the ends of a string passing over a pulley. The 4 kg mass is attached to the table top by another string. The tension in this string $T_1$ is equal to (take $g=10m/s^2)$

1. 10 N
2. 10.6 N
3. 25 N
4. 20 N

Q.

A body of mass m is suspended by two strings making angles $\alpha$ and $\beta$ with the horizontal (as shown in the figure). Find the tensions in the strings?

1. $T_2=\frac{gcos\beta }{sin(\alpha +\beta )};T_2=\frac{gcos\alpha }{sin(\alpha +\beta )}$

2. $T_2=\frac{mgcos\alpha }{sin(\alpha +\beta )};T_2=\frac{mgcos\beta }{sin(\alpha +\beta )}$

3. $T_1=\frac{mgcos\beta }{sin(\alpha +\beta )};T_2=\frac{mgcos\alpha }{sin(\alpha +\beta )}$

4. $T_2=mgcot\alpha ;T_2=mgtan\beta$

Q. A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass $m=0.4kg$ is at rest on this surface. An impulse of $1.0N$ s is applied to the block at time to $t=0$ so that it starts moving along the x-axis with a velocity $v\left(t\right)=v_0{e}^{\frac{-t}{\tau }}$, where $v_0$ is a constant and $\tau =4s$. The displacement of the block, in metres, at $t=\tau$ is .
[Take $e^{-1}=0.37$]

Q. A light rod is hinged (free to rotate) at its centre $O$ as shown in figure. Two point charges of same magnitude $+q$ are kept at its two ends. Rod is placed in uniform electric field $E$ as shown. Space is gravity free. Net torque about the hinge is

1. $2rqE$
2. $4rqE$
3. $3rqE$
4. Zero

Q. A force of $F=(5y+20)\hat{j}\text{N}$ acts on a particle. The work done by this force when the particle is moved from $y=0\text{m}\text{to}y=10\text{m}$ is ______$\text{J}$.

Q. Two blocks, each having a mass $\text{M}$, rest on frictionless surfaces as shown in the figure. If the pulleys are light and frictionless, and $\text{M}$ on the incline is allowed to move down along the incline, then the tension in the string will be

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

Q. A flexible chain of mass $m$ hangs between two fixed points $A$ and $B$ at the same level. The inclination of the chain with the horizontal at the two points of support is $\theta$. The tension at the midpoint $C$ of the chain is

1. $\frac{mg}{\tan \theta }$
2. $\frac{mg}{2\tan \theta }$
3. Zero
4. $\left(mg\right)\left(\frac{\sin \theta +\cos \theta }{2}\right)$

Q. What is the minimum value of $F$ needed so that block begins to move upward on frictionless incline plane as shown?

1. $Mg\tan \left(\frac{\theta }{2}\right)$
2. $Mg\cot \left(\frac{\theta }{2}\right)$
3. $\frac{Mg\sin \theta }{(1+\sin \theta )}$
4. $Mg\sin \left(\frac{\theta }{2}\right)$

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 ball is held at rest in position $A$ by two light cords. The horizontal cord is now cut and the ball swings to position $B$. What is the ratio of the tension in the cord at position $B$ to that at position $A$ originally?

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

Q. One end of a massless rope, which passes over a massless and frictionless pulley P is tied to a hook C while the other end is free. Maximum tension that the rope can bear is $840N$. With what value of maximum safe acceleration (in $m{s}^{-2})$ can a man of $60kg$ climb on the rope?

1. 16
2. 6
3. 4
4. 8

Q. Two blocks of mass $5kg$ and $3kg$ are tied with a heavy rope of mass $2kg$. An external force of $200N$ is applied on $5kg$ block and the whole system accelerates upwards. Find the tension at the midpoint of the rope?
(Take $g=10m/s^2$)

1. $80N$
2. $120N$
3. $100N$
4. $60N$

Q.

Two blocks of masses $2.9\text{kg}$ and $1.9\text{kg}$ are suspended from a rigid support by two inextensible wires each of length $1\text{m}$, the upper wire has negligible mass and the lower wire has a uniform mass of $0.2\text{kg/m}$. The whole system of block, wire and support has an upward acceleration of $0.2{\text{m/s}}^2$. (take $g=9.8m/se{c}^2$)

The tension at the mid-point of lower wire is:

1. $20\text{N}$
2. $20.4\text{N}$
3. $10.4\text{N}$
4. $30\text{N}$

Q.

An object is resting at the bottom of two strings which are inclined at an angle of ${120}^{\circ }$ with each other. Each string can withstand a tension of $20N$. The maximum weight of the object that can be sustained without breaking the strings is

1. $10N$
2. $20N$
3. $20\sqrt{2}N$
4. $40N$

Q. A rope of mass $5kg$ is moving vertically with an upward force of $100N$ acting at the upper end and a downward force of $70N$ acting at the lower end. The tension at the midpoint of the rope is
(Take $g=10m/s^2$)

1. $100N$
2. $85N$
3. $75N$
4. $105N$

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

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. A $10\text{kg}$ monkey is climbing a massless rope attached to a $15\text{kg}$ mass over a smooth tree limb. The mass is lying on the ground. In order to raise the mass from the ground he must climb with:

1. Acceleration greater than $5{\text{m/sec}}^2$
2. Acceleration greater than $2.5{\text{m/sec}}^2$
3. High speed
4. Acceleration greater than $10{\text{m/sec}}^2$

Q. Study the $v-t$ graph given here, plotted for a particle of mass $50\text{g}$. In which period will it have the maximum force?

1. $P$
2. $Q$
3. $R$
4. None of these

Q.

In a game of tug of war, a condition of equilibrium exists. Both the teams pull the rope with a force of 10⁴ N. Find the tension in the rope.

1. ${10}^{4}N$

2. ${10}^{5}N$

3. $0N$

4. $2\times {10}^{4}N$

Q. In the arrangement as shown, tension $T_2$ is ($g=10{\text{m/s}}^2$)

1. $50\text{N}$
2. $100\text{N}$
3. $50\sqrt{3}\text{N}$
4. $100\sqrt{3}\text{N}$

Q.

An object of mass 0.5 kg is whirled at the end of a string 0.8 m long. If the string makes three revolutions in 1.2 sec, find the tension on the string.