Spring Force

Q. The system shown in the figure is in equilibrium at rest and the spring and string are massless. Now the string is cut. The acceleration of masses $2\text{m}$ and $\text{m}$ just after the string is cut will be:

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

Q. Four infinite ladder network containing identical resistances of $R\Omega$ each, are combined as shown in figure. The equivalent resistance between $A$ and $B$ is $R_{AB}$ and between $A$ and $C$ is $R_{AC}$. If the value of $\frac{R_{AB}}{R_{AC}}$ is $\frac{x}{4}$, then the value of $8x$ is

Q. Two blocks A and B of masses $3m$ and $m$ respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively

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

Q. Q.1) A uniform ladder of mass m=40kg rests against a smooth vertical wall making an angle 30 degree with the horizontal. The lower end of ladder rests on a rough floor having mu=1/root 3.An electrician having mass80kg attempt climb the ladder to repair house wiring. Fraction of length that can be encountered by the electrician before the ladder begins to slip will be:- (a) 1/2 (b)1 (c)1/4 (d)1/3

Q. A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads $49\text{N}$ when the lift is stationary. If the lift moves downward with an acceleration of $5{\text{m/s}}^2$, the reading of the spring balance will be (Take $g=9.8m/s^2$)

1. $49\text{N}$
2. $24\text{N}$
3. $74\text{N}$
4. $15\text{N}$

Q. Four identical rectangular plates with length, $l=2\text{cm}$ and breadth, $b=3/2\text{cm}$ are arranged as shown in the figure. The equivalent capacitance between $P$ and $R$ is $\frac{x\times {10}^{-2}{ϵ}_0}{d}$ where $d$ is the distance between the plates in $\text{cm}$. The value of $x$ is ______.

$($Round off to the nearest integer$)$

Q. What is the equivalent capacitance of the system of capacitors between $\text{A}$ and $\text{B}$

1. 
   $\frac{7}{6}C$
2. 
   $1.6C$
3. 
   $C$
4. 
   $\text{None}$

Q.

A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body?

Q. The masses of 10 kg and 20 kg respectively are connected by a massless spring as shown in figure. A force of 200 N acts on the 20 kg mass. At the instant shown, the 10 kg mass has acceleration $12m/se{c}^2.$ What is the acceleration of 20 kg mass

1. 
2. 
3. 
4. 

Q. Find the reading of the spring balance for the figure shown. Take $g=10m/s^2$

1. $1.2kg$
2. $2.4kg$
3. $3.6kg$
4. $4.8kg$

Q. Two blocks $A$ and $B$ of masses $2m$ and $m$, respectively, are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in the figure. The magnitude of the acceleration of $A$ and $B$, immediately after the string is cut, are respectively

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

Q. The lengths of spring are $l_1$ and $l_2$ when stretched with forces of $4N$ and $5N$ respectively. Its natural length is

1. $2(l_1-l_2)$
2. $l_2+l_1$
3. $5(l_2-4l_1)$
4. $(5l_1-4l_2)$

Q.

What is the center of mass of a uniform rod?

Q. The atwood machine shown is suspended from a spring balance. The mass on one hanger is $M$, that on other is $(M+m)$. Suppose the heavier side (right side) hanger is fastened to the top of pulley by a thread. The scale reads $(2M+m)g$. The thread is burned and the system accelerates. The reading of spring balance now will be -

1. Same as before
2. Less than before
3. More than before
4. Can’t say

Q. A smooth semicircular wire track of radius $R$ is fixed in a vertical plane as shown in the figure. One end of a massless spring of natural length $\frac{3}{4}R$ is attached to the lowest point $O$ of the wire track. A small ring of mass m, which can slide on the track, is attached to the other end of the spring. The spring makes an angle of ${60}^0$ with the vertical. The spring constant is $k=\frac{mg}{R}$. Consider the instant when the ring is making an angle of ${60}^0$ with the vertical. Find the tangential acceleration of the ring.

1. $\frac{g5\sqrt{3}}{8}$
2. $\frac{g3\sqrt{3}}{8}$
3. $\frac{g5\sqrt{3}}{4}$
4. $\frac{g3\sqrt{3}}{4}$

Q. A block of mass $m$ placed on a smooth floor is connected to a fixed support with the help of a spring of stiffness $k$. It is pulled by a rope as shown in the figure. Tension force $T$ of the rope is increased gradually without changing its direction until the block losses contact from the floor. The increase in rope tension $T$ is so gradual that acceleration in the block can be neglected. What is the extension in the spring, when the block losses contact from the floor?

1. $\frac{mg\sin \theta }{k}$
2. $\frac{mg\tan \theta }{k}$
3. $\frac{mg\cos \theta }{k}$
4. $\frac{mg\cot \theta }{k}$

Q. A block of mass $20\text{kg}$ is suspended through two light spring balances as shown in figure. Calculate the reading of spring balance $\left(1\right)$ and $\left(2\right)$ respectively.

1. $200\text{N},400\text{N}$
2. $400\text{N},200\text{N}$
3. $0\text{N},200\text{N}$
4. $200\text{N},200\text{N}$

Q. Find the reading of the spring balance if it is assumed to be of negligible mass.
(Take $g=10m/s^2$)

1. $3kg$
2. $2kg$
3. $2.4kg$
4. $2.5kg$

Q. A 60 kg man stands on a spring scale in the lift. At some instant he finds, scale reading has changed from 60 kg to 50kg for a while and then comes back to the original mark. What should we conclude?

1. The lift was in constant motion downwards
2. The lift while in constant motion upwards, is stopped suddenly
3. The lift while in constant motion downwards, is suddenly stopped
4. The lift was in constant motion upwards

Q. In the figure a smooth pulley of negligible weight is suspended by a spring balance. Weights of $1\text{kg}$ and $5\text{kg}$ are attached to the opposite ends of a string passing over the pulley and move with acceleration because of gravity. During the motion, the spring balance reads a weight of

1. $6\text{kg}$
2. Less than $6\text{kg}$
3. More than $6\text{kg}$
4. May be more or less than $6\text{kg}$

Q.

The resistance across the legs M and N of the letter A as shown in the following figure is :

1. 20Ω

2. 8/3Ω

3. 4Ω

4. 32/3Ω

Q. A body of mass $25g$ is under water at a depth of $50cm$. If the specific gravity of material of body is $5$, the work necessary to lift the body slowly to the surface is (Consider $g=9.8\frac{m}{s^2}$ )

1. $980\times {10}^{5}erg$
2. $9.8\times {10}^{5}erg$
3. $980\times {10}^{6}erg$
4. $98\times {10}^{5}erg$

Q. As shown in the figure, two equal masses each of 2 kg are suspended from a spring balance. The reading of the spring balance will be

1. 2 kg
2. 4 kg
3. Between zero and 2 kg
4. Zero

Q. What is the acceleration of $3\text{kg}$ mass when acceleration of $2\text{kg}$ mass is $2{\text{m/s}}^2$ as shown ?

1. $3{\text{m/s}}^2$
2. $0.5{\text{m/s}}^2$
3. Zero
4. $2{\text{m/s}}^2$

Q. A body of mass 5 kg is suspended by a spring balance on a frictionless inclined plane as shown in the figure. The spring balance measures

1. 50 N
2. 25 N
3. 500 N
4. 10 N

Q. A block of mass $2kg$ is suspended from the ceiling through a massless spring of spring constant $k=100\text{N/m}$. What will be the difference in the elongation of the spring, if another $1kg$ mass is added to the mass of the block?
(Take $g=10m/s^2$)

1. $0.3\text{m}$
2. $0.5\text{m}$
3. $0.2\text{m}$
4. $0.1\text{m}$

Q. Two blocks $A$ and $B$ of masses $m$ and $2m$ respectively are held at rest such that the spring is in natural length. Find out the accelerations of both the blocks just after release:

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

Q. The mass of silver coin is 10 gram. A person can carry a load of 40kg. How many persons will be required to carry one Avocado number of such coins?

Q. The system is released from rest with both the springs in unstretched position. Mass of each block is $5\text{kg}$ and force constant of each spring is $10\text{N/m}$. Assume pulley and strings are massless and all contacts are smooth. Take $g=10{\text{m/s}}^2$

1. Extension in horizontal spring at equilibrium is $2\text{m}$
2. Compression in vertical spring at equilibrium is $1\text{m}$
3. Compression in vertical spring at equilibrium is $2\text{m}$
4. Extension in horizontal spring at equilibrium is $3\text{m}$

Q. A $\text{4 kg}$ block is connected with two springs of force constants $k_1=100{\text{Nm}}^{-1}$ and $k_2=300{\text{Nm}}^{-1}$ as shown in figure. The block is released from rest with the springs unstretched. The acceleration of the block in its lowest postion is $(g=10{\text{ms}}^{-2})$

1. $\text{zero}$
2. $5{\text{ms}}^{-2}$ $\text{upwards}$
3. $10{\text{ms}}^{-2}$ $\text{downwards}$
4. $10{\text{ms}}^{-2}$$\text{upwards}$