Ropes

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

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.

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

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

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. 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 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. Consider a rope of total mass $M$ and length $L$ suspended at rest from a fixed mount. The rope has a linear mass density that varies with height as $\lambda \left(z\right)={\lambda }_0\sin (\pi z\setminus L)$, where ${\lambda }_0$ is a constant. Constant gravitational acceleration $g$ acts downward, then constant ${\lambda }_0$ is

1. $\frac{\pi M}{2L}$
2. $\frac{\pi M}{3L}$
3. $\frac{\pi M}{4L}$
4. $\frac{2\pi M}{L}$