Ropes

Q. The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

1. are not equal to each other in magnitude.
2. cannot be predicted.
3. are equal to each other.
   
4. are equal to each other in magnitude.

Q. A block of mass $m$ is resting on a smooth horizontal surface. One end of a uniform rope of mass $\left(m/3\right)$ is fixed to the block, which is pulled in the horizontal direction by applying a force $F$ at the other end. The tension in the middle of the rope is

1. $\frac{8}{7}F$
2. $\frac{1}{7}F$
3. $\frac{1}{8}F$
4. $\frac{7}{8}F$

Q.

What are internal and external forces?

Q. A thermodynamic system is taken through the cycle PQRSP process. The net work done by the system is

1. 20 J
2. -20 J
3. 400 J
4. -374 J

Q. A uniform rope of length $L$ and mass $M$ is hanging from a rigid support. The tension in the rope at a distance $x$ from the rigid support is

1. $Mg$
2. $Mg\left(\frac{L}{L-x}\right)$
3. $Mg\left(\frac{L-x}{L}\right)$
4. $Mg\left(\frac{x}{L}\right)$

Q. A hanging mass $M$ is connected to a four times bigger mass by using a string-pulley arrangement, as shown in figure. the bigger mass is placed on a horizontal ice-slab and being pulled by $2Mg$ force. In this situation, tension in the string is $\frac{x}{5}Mg$ for $x=$
Neglect mass of the string and friction of the block (bigger mass) with ice slab. (Given g = acceleration due to gravity)

Q. A mass m is suspended from a spring of length l and force constant K. The frequency of vibration of the mass is $f_1$ . The spring is cut into two equal parts and the same mass is suspended from one of the parts. The new frequency of vibration of mass is $f_2$. Which of the following relations between the frequencies is correct?

1. 
2. 
3. 
4. 

Q.

Two blocks $A$ and $B$ of masses $m$ and $2m$ respectively are held at rest such that the spring is at its natural length. Find out the accelerations of blocks $A$ and $B$ respectively just after release (pulley, string and spring are massless).

1. $g$↓, $g$↓
2. $\frac{g}{3}\downarrow ,\frac{g}{3}\downarrow$
3. $0$, $0$
4. $g$↓, $0$

Q. A mass of 1 kg is suspended by a string A. Another string C is connected to its lower end (see figure). If a sudden jerk is given to C, then

1. The portion BC of the string will break
2. None of the strings will break
3. The mass will start rotating
4. The portion AB of the string will break

Q. Two bodies M and N of equal masses are suspended from two separate massless springs of force constants $k_1$ and $k_2$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude M to that of N is

1. 
2. 
3. 
4. 

Q. At what minimum acceleration should a monkey slide down a rope whose breaking strength is two-thirds of the monkey's weight?

1. g
2. 
3. 2g
4. 

Q.

The pulley shown in figure (10-E8) has a radius 10 cm and moment of inertia 0.5 kg-$m^2$ about its axis. Assuming the inclined planes to be frictionless, calculate the acceleration of the 4.0 kg block.

Q. In the figure shown, find the tension at the midpoint of the rope of mass $2\text{kg}$ connecting the masses $3\text{kg}$ and $5\text{kg}$. Given $F=30N$.

1. $10\text{N}$
2. $11\text{N}$
3. $12\text{N}$
4. $15\text{N}$

Q.

A uniform metre stick of mass 200 g is suspended from the ceiling through 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.

Q. Consider the three cases given in figures shown. Assume the friction to be absent everywhere and the pulleys to be light; the string connecting the blocks to another block. or fixed vertical wall to be light and inextensible. Let $T_A,T_B\text{and}{T}_C$ be the tension in the strings in, $figureA,figureB\text{and}figureC$ respectively. Then pick the correct comparison between the given tensions (for the instant shown from options below,

1. $T_A=T_B=T_C$
2. $T_B=T_C<T_A$
3. $T_A<T_B<T_C$
4. $T_B<T_C<T_A$

Q. A block of mass $m\text{kg}$ is suspended by a string attached with a $2m\text{kg}$ mass block. The $2m$ mass block is suspended by a spring as shown in the figure. The system is initially at equilibrium and rest. The spring and string are massless. Now the string is cut. The accelerations of mass $2m$ and $m$ just after the string is cut will be

1. $\frac{g}{2}$ upwards, $g$ downwards
2. $g$ downwards, $\frac{g}{2}$ upwards
3. $g$ downwards, $2g$ downwards
4. $2g$ upwards, $g$ downwards

Q.

A force of 750 N is applied to a block of mass 102 kg to prevent it from sliding on a plane with an inclination angle ${30}^o$ with the horizontal. If the coefficients of static friction and kinetic friction between the block and the plane are 0.4 and 0.3 respectively, then the frictional force acting on the block is

1. 750 N

2. 500 N

3. 345 N

4. 250 N

Q. System shown in figure is in equilibrium. Find the magnitude of net change in the string tension between two masses just after, when one of the springs is cut. Mass of both the blocks is same and equal to m and spring constant of both springs is k. Report n, if answer is mg/n

Q. A circular wheel comprises a ring of radius $R$ and mass $M$ and three spokes of mass $m$ and length $R$ each. The moment of inertia of the wheel about its axis passing through its centre and perpendicular to its plane is

1. $(M+\frac{m}{4})R^2$
2. $(M+m)R^2$
3. $(M+3m)R^2$
4. $\left(\frac{M+m}{2}\right)R^2$

Q. A rope of length $L$ has its mass per unit length $\lambda$ vary according to the function $\lambda \left(x\right)=e^{x/L}$. The rope is pulled by a constant force of $1\text{N}$ on a smooth horizontal surface. The tension in the rope at $x=L/2$ is: (Take $e=2.7$)

1. $0.50\text{N}$
2. $0.38\text{N}$
3. $0.62\text{N}$
4. None

Q.

A block of weight W is suspended by a string of fixed length. The ends of the string are held at various positions as shown in the figures below. In which case, if any, is the magnitude of the tension along the string largest?

1. 

2. 

3. 

4. 

Q.

A fireman wants to slide down a rope. The rope can bear a tension of $\frac{3}{4}$ of the weight of the man. With what minimum acceleration should the fireman slide down?

1. $\frac{g}{2}$

2. $\frac{g}{3}$

3. $\frac{g}{4}$

4. $\frac{g}{6}$

Q. Two blocks of mass 2.9 kg and 1.9 kg are suspended from a rigid support S by two inextensible wires each of length 1 meter, as shown in the figure. The upper wire has negligible mass and the lower wire has a uniform mass of 0.2 kg/m. The whole system of blocks, wires and support have an upward acceleration of 0.2 $m/s^2$. Acceleration due to gravity is 9.8 $m/s^2$. Then the difference in tension at the mid point's (in N) of the upper wire and the lower wire is

Q. With what minimum acceleration can a fireman slide down a rope while breaking strength of the rope is $\frac{2}{3}$ of his weight

1. 
2. 
3. 
4. 

Q. A sphere of weight 50 N is resting in a V - shaped groove as shown in figure and is subjected to a spring force. The spring is compressed to a length of 120 mm from the free length of 160 mm. If the stiffness of spring is 2 N/mm the diffrence (magnitude, correct two decimal place) of the support reactions is ____.

1. 47

Q. A $50kg$ person stand on a $25kg$ platform. He pulls on the rope which is attached to the platform via the frictionless pulleys as shown in the figure. The platform moves upwards at a steady rate if the force (in $N$) with which the person pulls the rope is

Q. The figure below shows a uniform rod of length $30\text{cm}$ having a mass of $3.0\text{kg}.$ The strings as shown in the figure are pulled by constant forces of $20\text{N}$ and $32\text{N}$. Find the force exerted by the $20\text{cm}$ part of the rod on the $10\text{cm}$ part. All the surfaces are smooth, and the strings are light.

1. $64\text{N}$
2. $12\text{N}$
3. $24\text{N}$
4. $36\text{N}$

Q.

Two blocks $A$ and $B$ of masses $m$ and $2m$ respectively are held at rest such that the spring is at its natural length. Find out the accelerations of blocks $A$ and $B$ respectively just after release (pulley, string and spring are massless).

1. $g$↓, $g$↓
2. $\frac{g}{3}\downarrow ,\frac{g}{3}\downarrow$
3. $0$, $0$
4. $g$↓, $0$

Q.

Two bodies M and N of equal masses are suspended from two separate massless springs of force constants $k_1$ and $k_2$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude M to that of N is

1. 

2. 

3. 

4. 

Q. The figure below shows a uniform rod of length $30\text{cm}$ having a mass of $3.0\text{kg}.$ The strings as shown in the figure are pulled by constant forces of $20\text{N}$ and $32\text{N}$. Find the force exerted by the $20\text{cm}$ part of the rod on the $10\text{cm}$ part. All the surfaces are smooth, and the strings are light.

1. $64\text{N}$
2. $24\text{N}$
3. $36\text{N}$
4. $12\text{N}$