Tension in a String

Q.

A string of length $L$ is fixed at one end and carries a mass $M$ at the other end. The string makes $\frac{2}{\pi }$ revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is

1. ML

2. 16 ML

3. 2 ML

4. 4 ML

Q. A heavy block of mass M hangs in equilibrium at the end of a rope of mass m and length I connected to aceiling. Determine the tension in the rope at a distance x from the ceiling.

Q. as we know surface tension = force / length. then what is s= pgrh/2 the formula of surface tension ?

Q. A boy of mass 40 kg is hanging from a horizontalbranch of a tree. The tension in his arms isminimum when the angle between the arms is :-(1) 0^° (2) 90^° (4) 180^° (3) 120

Q.

A body of weight 100 N is suspended with the help of strings as shown in figure. The tensions T₁ and T₂ will be

1. T₁ = 73.2 N, T₂ = 89.65 N

2. T₁ = 10.2 N, T₂ = 20.2 N

3. T₁ = 100 N, T₂ = 200 N

4. T₁ = 70.2 N, T₂ = 80.65 N

Q.

A horizontal force of 100 N pulls two masses 5 kg and 10 kg tied to each other by a light string. What is the tension in the string if the force is applied on 10 kg mass?

1. 33.3 N

2. 43 N

3. 23 N

4. 30 N

Q. 144.A uniform rod AB of weight W is hinged to a fixed point A.it is held in horizontal position by a string, one end of which is attached to B as shown in the picture.find in terms of W, the tension of the string?

Q. In the figure shown, find the tension $T_1$, if all surfaces are smooth. Take $g=10{\text{m/s}}^2$.

1. $20\text{N}$
2. $30\text{N}$
3. $50\text{N}$
4. $60\text{N}$

Q. Q. An external force of 20 N acts at an angle of 60^{0 }with the normal to the surface of a sqare plate having each side of length 20 cm. what is the stress produced in the plate?

Q. 20.Calculate the acceleration of the masses 12kg shown in figure. Also calculate the tension in the string connecting the 12kg mass the string are massless and unextensible. Pulleys are massless and frictionless

Q. A 100g ball having speed 10 m/s collides with a wall and rebounds with the same speed and the contact period between the wall and the ball is 0.1 second, then the force expereienced by the wall is

Q. 68 The displacement x of a body having relation with timeasx=3t^2-6t+7, then distance covered by the body inthefirsttwosecondis\lbrack wherexisinmeterandtisinsecond\rbrack?

Q. ASSERTION- One end of ideal massless spring is connected to fixed vertical wall and other end to a block of mass m initially at rest on a smooth horizontal surface. The spring is initially in natural length. Now a horizontal force F acts on the block. Then the maximum extension in spring is equal to maximum compression in spring. REASON- To compress or to expand an unstretched spring by equal amount , same work is done on spring

Q.

A pendulum bob has a speed 3m/swhile passing through its lowest position. What is its speed when it makes on angle of ${60}^{\circ }$ with the vertical? The length of the pendulum is 0.5m. Take g = 10 m/$s^2$.

1. 1 m/s

2. 2 m/s

3. 4 m/s

4. 0 m/s

Q. Two blocks tied with a massless string of length $3\text{m}$ are placed on a table rotating at an angular speed $\omega =4\text{rad/s}$. The axis of rotation is $1\text{m}$ from the block having $1\text{kg}$ mass. Assume that the surface below $2\text{kg}$ block is smooth and that below the $1\text{kg}$ block is rough. Find the tension $\left(T\right)$ in the string and the frictional force$\left(f\right)$ acting on the $1\text{kg}$ block. Take $g=10{\text{m/s}}^2$

1. $T=64\text{N},f=48\text{N}$
2. $T=48\text{N},f=64\text{N}$
3. $T=8\text{N},f=4\text{N}$
4. $T=4\text{N},f=8\text{N}$

Q. The position of a moving particle is given by equation x=(t^2+3t-5)m, then displacement of particle between t=1 second to t=2 second is 1)+4m 2)-4m 3)-6m 4)6m

Q. Two blocks of masses $5\text{kg}$ and $2\text{kg}$ are connected by a massless string as shown in figure. A vertical force $F$ is applied on the $5\text{kg}$ block. Find the value of $F$ if tension in the string is $40\text{N}$. $(g=10{\text{m/s}}^2)$

1. $140\text{N}$
2. $70\text{N}$
3. $40\text{N}$
4. $100\text{N}$

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 $0.2{\text{m/s}}^2$.
The tension at the mid-point of lower wire is:

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

Q. Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force F = 600 N is applied to (i) A, (ii) B along the direction of string. What is the tension in the string in each case?

Q. A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string ? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N ?

Q. Two blocks of masses $5\text{kg}$ and $2\text{kg}$ are connected by a massless string as shown in figure. A vertical force $F$ is applied on the $5\text{kg}$ block. Find the value of $F$ if tension in the string is $40\text{N}$. $(g=10{\text{m/s}}^2)$

1. $140\text{N}$
2. $70\text{N}$
3. $40\text{N}$
4. $100\text{N}$

Q. Consider the situation shown in the figure, find the tension in string $AB$ considering the pulley and string as frictionless and massless:

1. $3\text{N}$
2. $2\text{N}$
3. $8\text{N}$
4. Zero

Q. 34.An elevator and its load have a total mass of 800 kg. Find the tension in the supporting cable when the elevator, moving downward at 10 m/s, is brought to rest with constant acceleration in a distance of 25 m. (Take g = 10 m/s2) :- (1) 6400 N (2) 8000 N (3) 9600 N (4) Zero

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. The blocks $(m_2>m_1)$ are held in such a manner that spring is unstretched initially. Consider the situation at the time of release of the block $(t=0)$ and short time after releasing the block $(t>0)$. Accelerations of the blocks of masses $m_1$ and $m_2$ are $a_1$ and $a_2$ respectively

1. $t=0,a_1=a_2$
2. $t=0,a_1<a_2$
3. $t>0,a_1=a_2$
4. $t>0,a_1<a_2$

Q. The acceleration of blocks $m_1,m_2,m_3$ blocks as shown in figure given below will be:

1. $\frac{F}{m_2}$
   
2. $\frac{F}{m_1+m_2}$
   
3. $\frac{F}{m_1+m_2+m_3}$
   
4. $\frac{F}{m_1+2m_2+m_3}$
   

Q. A uniform rope of mass $M$ and length $L$ is accelerated upwards with acceleration ${}^{\prime }{a}^{\prime }$ by applying force on the topmost point. What is the tension in the rope at a distance $X$ from the lower end?

1. $\frac{M}{L}\times a$
2. $\frac{M}{L}X(g+a)$
3. $\frac{M}{L}(L-X)a$
4. None

Q. In the figure below, all surfaces are assumed to be smooth and the force $F=100N$. If the acceleration of block $B$ of mass $20kg$ is '$a$' and tension in the string connecting block $A$ of mass $20kg$ is $T$, then just after force $F$ is applied,

1. $T=0$ and $a=5m/s^2$
2. $T=100N$ and $a=0$
3. $T=200N$ and $a=5m/s^2$
4. $T=100N$ and $a=5m/s^2$

Q. If ${\mu }_s\text{and}{\mu }_k$ represent the coefficients of static and kinetic friction with appropriate suffixes for the two bodies shown, find the acceleration of the system. Take $g=10m/s^2$.

1. $\text{Zero}$
2. $4.2m/s^2$
3. $5.2m/s^2$
4. $10m/s^2$

Q. A uniform metre stick of mass 200 g is suspended from the ceiling thorough two vertical strings of equal lengths fixed at the ends. A small object of mass 20 g is placed on the stick at a distance of 70 cm from the left end. Find the tensions in the two strings.