Spring Force

Q. Force constant of a spring is $100\text{N/m}$. If both the blocks of mass $10\text{kg}$ and $12\text{kg}$ attached with spring and string are at rest. Then find the extension in spring. Take $g=10{\text{m/s}}^2$.

1. $1.1\text{m}$
2. $2.2\text{m}$
3. $3.3\text{m}$
4. $1.2\text{m}$

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. $2.5kg$
4. $2.4kg$

Q. For the given system, find the extension in the spring if $m_1=4\text{kg}$ and $m_2=6\text{kg}$. Take $g=10{\text{m/s}}^2$.

1. $0.96\text{m}$
2. $0.86\text{m}$
3. $0.48\text{m}$
4. $0.24\text{m}$

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

Q. Find the reading of the spring balance if $M$ is in equilibrium. Assume all surfaces to be smooth. Take $g=10{\text{m/s}}^2$.

1. $1kg$
2. $1.2kg$
3. $1.4kg$
4. $1.6kg$

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

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. More than before
3. Less than before
4. Can’t say

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

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 $m_2$ is loaded onto another block $m_1$ placed on a spring of stiffness $k$ as shown in the figure. If block $m_2$ is suddenly removed, then magnitude of acceleration of block $m_1$ just after the removal of $m_2$ will be:

1. $\frac{\sqrt{m_1{m}_2}}{m_1+m_{2}g}$
2. $\left(\frac{m_2}{m_1}g\right)$
3. $\left(\frac{m_1}{m_2}g\right)$
4. $\frac{m_1+m_2}{m_1-m_2}$

Q. Find the reading of the spring balance if $M$ is in equilibrium. Assume all surfaces to be smooth. Take $g=10{\text{m/s}}^2$.

1. $1kg$
2. $1.2kg$
3. $1.4kg$
4. $1.6kg$

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. A pulley system is connected as shown in the figure. If the spring is elongated by a distance of $0.02\text{m}$, then what is the force constant of the spring? (Assume that the spring does not affect the overall acceleration of the bodies.)

1. $200\text{N/m}$
2. $8000\text{N/m}$
3. $2000\text{N/m}$
4. $800\text{N/m}$

Q. The work done by an external agent in stretching a spring of force constant $K$ from length $l$ to $3l$ is

1. $8K{l}^2$
2. $4K{l}^2$
3. $2Kl$
4. $\frac{K}{4l}$

Q. Two blocks $A$ and $B$ of same mass $m$ attached with a light spring are suspended by a string as shown in the figure. Find the acceleration of block $A$ and $B$ respectively, just after the string is cut.

1. $g$ upwards, $g$ downwards
2. $g$ downwards, zero
3. $2g$ upwards, $g$ upwards
4. $2g$ downwards, zero

Q. What is the equivalent spring constant for the syatem shown below in the figure?
(All the springs are ideal and identical having spring constant $k\text{N/m}$)

1. $\frac{6k}{7}$
2. $\frac{3k}{5}$
3. $\frac{2k}{5}$
4. $2k$

Q. Force constant of a spring is $100\text{N/m}$. If both the blocks of mass $10\text{kg}$ and $12\text{kg}$ attached with spring and string are at rest. Then find the extension in spring. Take $g=10{\text{m/s}}^2$.

1. $1.1\text{m}$
2. $2.2\text{m}$
3. $3.3\text{m}$
4. $1.2\text{m}$

Q. Figure shows a block of mass $m$ attached to a spring of force constant $k$ and connected to ground by two string. In relaxed state natural length of the spring is $l$. In the situation shown in figure, find the tension in the strings (1) and (2).

1. $T_1=\frac{1}{4}[kl-2\text{mg}],T_2=\frac{\sqrt{3}}{4}[kl-2\text{mg}]$
2. $T_1=\sqrt{3}[kl-2\text{mg}],T_2=[kl-2\text{mg}]$
3. $T_1=\frac{\sqrt{3}}{4}[kl-2\text{mg}],T_2=\frac{1}{4}[kl-2\text{mg}]$
4. $T_1=[kl-2\text{mg}],T_2=\sqrt{3}[kl-2\text{mg}]$

Q. Find the elongation in the spring for the system shown in the figure. ($g=10m/s^2$)

1. $25\text{cm}$
2. $50\text{cm}$
3. $75\text{cm}$
4. $100\text{cm}$

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. $12m/se{c}^2$
2. $4m/se{c}^2$
3. $10m/se{c}^2$
4. $Zero$

Q. What is the equivalent spring constant for the syatem shown below in the figure?
(All the springs are ideal and identical having spring constant $k\text{N/m}$)

1. $\frac{6k}{7}$
2. $\frac{3k}{5}$
3. $\frac{2k}{5}$
4. $2k$

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 $m\text{kg}$ is attached to a massless spring of spring constant $k\text{N/m}$. This system is accelerated upwards with an acceleration $a{\text{m/s}}^2$. Then the elongation in spring will be (in metres):

1. $\frac{mg}{k}$
2. $\frac{m(g-a)}{k}$
3. $\frac{m(g+a)}{k}$
4. $\frac{ma}{k}$

Q. Two blocks A of mass $10\text{kg}$ and block B are connected to each other as shown in the figure. The pulley is frictionless. The coefficient of friction between the surfaces is $0.3$. If the spring is stretched by $1\text{cm}$ and friction is maximum, Calculate the spring constant $\left(k\right)$ of the spring shown in the figure.

1. $2000\text{N/m}$
2. $3000\text{N/m}$
   
3. $2500\text{N/m}$
4. $3500\text{N/m}$

Q. What is the equivalent spring constant for the syatem shown below in the figure?

1. $\frac{5k}{6}$
2. $\frac{6k}{5}$
3. $\frac{2k}{3}$
4. $\frac{3k}{2}$

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}$

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. What is the extension in the spring? (Given spring constant= k, mass of man= m.)

1. Zero
2. mg/k
3. k/mg
4. 2kg/m

Q. An object of mass $5\text{kg}$ is attached to the hook of a spring balance and the balance is suspended vertically from the roof of a lift. The reading on the spring balance when the lift is going up with an acceleration of $0.25{\text{m/s}}^2$ is $(g=10{\text{m/s}}^2)$

1. $51.25\text{N}$
2. $48.75\text{N}$
3. $52.75\text{N}$
4. $47.25\text{N}$

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. $\frac{g3\sqrt{3}}{4}$