Combination of Springs

Q. What is the equivalent spring constant for the system shown below?

1. $5k$
2. $3.5k$
3. $1.5k$
4. $0.5k$

Q. The system shown is in equilibrium. Find the accelerations of the blocks A, B and C just after the spring between B and C is cut. All blocks are of equal masses $‘m^{\prime }$ each and springs are of equal stiffness. (Assume springs to be ideal and take downward acceleration to be positive).

1. $+g,+g,-g$
2. $-\frac{g}{2},-\frac{g}{2},+g$
3. $+g,-\frac{g}{2},-g$
4. $0,-\frac{g}{2},-g$

Q. The system shown is in equilibrium. Find the acceleration of the block C at the instant just after the spring between ceiling and A is cut. All blocks are of equal masses ‘$m$’ each and springs are of equal stiffness. (Assume springs to be ideal).

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

Q. For the given figure List - I gives acceleration of blocks of masses $m_1,m_2,m_3\&m_4$ and List - II gives their magnitudes. Here $m_1=m_2=2m$ and $m_3=m_4=m$

$\begin{array}{cc}\text{List - I}& \text{List - II}\\ \text{(I)}{a}_1& \text{(P)}2g\\ \text{(II)}{a}_2& \text{(Q)}g\\ \text{(III)}{a}_3& \text{(R)}\frac{g}{2}\\ \text{(IV)}{a}_4& \text{(S)}\frac{g}{4}\\ & \text{(T)}0\\ & \text{(U)}\text{None}\end{array}$
Just after cutting string connecting $m_1$ and $m_2$ correct match for accelerations of blocks is

1. $I\to Q;II\to Q;III\to P;IV\to Q$
2. $I\to Q;II\to P;III\to R;IV\to T$
3. $I\to Q;II\to Q;III\to T;IV\to T$
4. $I\to P;II\to Q;III\to R;IV\to U$

Q.

The given setup is in equilibrium springs were in natural length before force was applied. If I have to replace the above setup of 1 block and 2 springs by 1 block and 1 spring, What will be the spring constant of that new spring, such that the block is displaced by the same amount as previously.

1. $K_1=K_2+K_3$

2. $\frac{K_3(K_1+K_2)}{K_1+K_2+K_3}$

3. $\frac{K_1{K}_2+K_2{K}_3}{K_1+K_2+K_3}$

4. $\frac{1}{K_1}+\frac{1}{K_2}+\frac{1}{K_3}$

Q. The system shown is in equilibrium. Find the acceleration of the block C at the instant just after the spring between ceiling and A is cut. All blocks are of equal masses ‘$m$’ each and springs are of equal stiffness. (Assume springs to be ideal).

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

Q. A block of mass 10 kg is suspended through two light springs which are balanced as shown in the figure. Then

1. both the scales will read 10 kg.
2. both the scales will read 5 kg.
3. the upper scale will read 10 kg and the lower one zero.
4. the readings may be of any value, but their sum will be 10 kg.

Q. For the spring block arrangement as shown in figure:


Given that $k_1=2k_2$. If force applied by the first spring on the block is $F_1$ and force applied by the second spring on the block is $F_2$, choose the correct option(s) if the block is in equilibrium with the action of an external force $30\text{N}$ on the block.

1. $x_1=2x_2$
2. $x_1=x_2$
3. $F_1=F_2=30\text{N}$
4. $F_1=20\text{N},F_2=10\text{N}$