Spring Potential Energy

Q. If a spring extends by $x$ on loading, then energy stored by the spring is (Given: $T$ is the tension in spring and $k$ is spring constant)

1. $\frac{T^2}{4k}$
2. $\frac{2T^2}{k}$
3. $\frac{T^2}{2k}$
4. $\frac{T^2}{k}$

Q. Two springs A and B having spring constants $k_A$ and $k_B(k_A=4k_B)$ are stretched by applying force of equal magnitude. If energy stored in spring A is $E_A$, then energy stored in B will be:

1. $2E_A$
2. $\frac{E_A}{4}$
3. $\frac{E_A}{2}$
4. $4E_A$

Q.

A spring of force constant $800N/m$ has an extension of $5cm$. Find work done in extending it from $5cm$ to $15cm$.

Q.

A compressed or elongated spring have which kind of energy? Can this be negative?

Q.
From a semicircular disc of mass m and radius R a circular portion of radius $\frac{R}{2}$ is removed as shown in figure then moment of inertia of remaining portion about diameter of semicircle as shown in figure is $\frac{m{R}^2}{n}$. Here n is (Write upto two digits after the decimal point.)

Q. Two springs $A$ and $B$ are stretched by applying forces of equal magnitudes. If the energy stored in $A$ is E, then the energy stored in B will be-
(Given relation between spring constants of $A$ and $B$ is $(k_A=2k_B)$)

1. $\frac{E}{2}$
2. $2E$
3. $E$
4. $\frac{E}{4}$

Q. A spring of spring constant $5\times {10}^3\text{N/m}$ is stretched initially by $5\text{cm}$ from the unstretched position. The work required to further stretch the spring by another $5\text{cm}$ is:

1. $6.24\text{N-m}$
2. $12.50\text{N-m}$
3. $18.75\text{N-m}$
4. $25.00\text{N-m}$

Q. In the shown figure, the bill A is released from rest, when the spring is at its natural (unstretched) length. For the block B of mass M to leave contact with ground at some stage, the minimum mass of A must be

1. M
2. 2M
3. M/4
4. M/2

Q. Let $T_1$ and $T_2$ be the time periods of springs $A$ and $B$ when mass $M$ is suspended from one end of each spring. If both springs are taken in series and the same mass $M$ is suspended from the series combination, the time period is $T$, then:

1. $T^2=T_1^2+T_2^2$
2. $\frac{1}{T}=\frac{1}{T_1}+\frac{1}{T_2}$
3. $\frac{1}{T^2}=\frac{1}{T_1^2}+\frac{1}{T_2^2}$
4. $T_1+T_2+T_3$

Q. The force constant of a weightless spring is $16N/m$. A body of mass $1.0kg$ suspended from it is pulled down through $5cm$ & then released. The maximum kinetic energy of the system(spring $+$ body) will be?

1. $2\times {10}^{-2}J$
2. $4\times {10}^{-2}J$
3. $8\times {10}^{-2}J$
4. $16\times {10}^{-2}J$

Q. A spring $40\text{mm}$ long is stretched by applying a force. If $10\text{N}$ force is required to stretch the spring through $1\text{mm}$, then work done in stretching the spring through $40\text{mm}$ is

1. $24\text{J}$
2. $8\text{J}$
3. $56\text{J}$
4. $64\text{J}$

Q. Two threaded bolts A and B of same material and length are subjected to identical tensile load. If the elastic energy stored in bolt A is 4 times that of the bolt B and the mean diameter of bolt A is 12 mm, the mean diameter of bolt B in mm is

1. 16
   
2. 24
3. 36
4. 48

Q. It takes a force of $10$ N to stretch a spring $2$ m beyond its natural length. How much work (in N.m) is done in stretching the spring $4$ m from its natural length?

1. $20$
2. $40$
3. $30$
4. $80$

Q. Two springs of spring constants $1500N/m$ and $3000N/m$ respectively are stretched with the same force. They will have the potential energies in the ratio:

1. $1:2$
   
2. $2:1$
   
3. $1:4$
   
4. $4:1$
   

Q. A spring $40\text{mm}$ long is stretched by applying a force. If $10\text{N}$ force is required to stretch the spring through $1\text{mm}$, then work done in stretching the spring through $40\text{mm}$ is

1. $24\text{J}$
2. $8\text{J}$
3. $56\text{J}$
4. $64\text{J}$

Q. Two blocks of mass $3kg$ and $6kg$ respectively are placed on a smooth horizontal surface. They are connected by a light spring of force constant $k=200N/m$. Initially the spring is unstretched and the indicated velocities are imparted to the blocks. Find maximum extension of the spring in $cm$ ?

Q. In order to raise a block of mass $100$ kg a man of mass $60$ kg fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration $\frac{5g}{4}$ relative to rope. The tension in the rope is $(g=10m{s}^{-2})$.

Q. A block of mass $1kg$ falls from a height of $5m$ on a vertical spring fastened to a horizontal board placed on the floor. If the spring constant of the spring is $10N/m$, the maximum compression that the spring undergoes is:

1. $1.7m$
2. $3.4m$
3. $4.3m$
4. $0.43m$

Q. Three blocks of masses $4kg,6kg$ and $8kg$ are hanging over a fixed pulley as shown. The tension in the string connecting $4kg$ and$6kg$ block is
($g=10m/s^2$)

1. $4N$
2. $6N$
3. $\frac{320}{g}N$
4. $\frac{40}{9}N$

Q. If a spring extends by $x$ on loading, then energy stored by the spring is (Given: $T$ is the tension in spring and $k$ is spring constant)

1. $\frac{T^2}{4k}$
2. $\frac{2T^2}{k}$
3. $\frac{T^2}{2k}$
4. $\frac{T^2}{k}$

Q. The work done in stretching a spring of force constant $k$ from length $l_1$ to $l_2$ is

1. $k(l_2-l_1)$
2. $k/2(l_2-l_1)$
3. $k(l_2^2-l_1^2)$
4. $\frac{1}{2}k(l_2^2-l_1^2)$

Q. A spring $40\text{mm}$ long is stretched by applying a force. If $10\text{N}$ force is required to stretch the spring through $1\text{mm}$, then work done in stretching the spring through $40\text{mm}$ is

1. $24\text{J}$
2. $8\text{J}$
3. $56\text{J}$
4. $64\text{J}$

Q. If the spring extended by $x$ on loading, then the energy stored by the spring is (If T is the tension in the spring):

1. $\frac{T^2}{2x}$
2. $\frac{2T^2}{k}$
3. $\frac{2k}{T^2}$
4. $\frac{T^2}{2k}$

Q. If a spring extends by $x$ on loading, then energy stored by the spring is (Given: $T$ is the tension in spring and $k$ is spring constant)

1. $\frac{T^2}{4k}$
2. $\frac{2T^2}{k}$
3. $\frac{T^2}{2k}$
4. $\frac{T^2}{k}$

Q.

If $m_1=20kg\&m_2=10kg$ find the normal force acting on the floor as shown in fig.?

1. 200 N
2. None of these
3. 300 N
4. 100 N

Q. If a spring extends by $x$ on loading then energy stored by the spring is:- ($T$ is the tension in the spring, $k$ is spring constant)

1. $\frac{T^2}{2x}$
2. $\frac{T^2}{2k}$
3. $\frac{2k}{T^2}$
4. $\frac{{2T}^2}{k}$

Q. A 1 kg mass executes SHM with an amplitude 10 cm, it takes $2\pi$ seconds to go from one end to the other end. The magnitude of the force acting on it at any end is :

1. 0.1 N
2. 0.2 N
3. 0.5 N
4. 0.05 N

Q. A body of mass $50g$ is moving with a velocity of $10m{s}^{-1}$. It is brought to rest by a resistive force of $10N$. Find the distance that the body will travel after the resistance force is applied.

Q. A wire is suspended by one end. At the other end, a weight equivalent to 20 N force is applied. If the increase in length is I mm, then increase in the f the wire will be

1. 0.01 J
2. $0.02J$
3. $0.04J$
4. $1.00J$

Q. Force constants of two wires A and B of the same material are $K$ and $2K$ respectively. If two wires are stretched equally, then the ratio of work done in stretching $\left(\frac{W_A}{W_B}\right)$ is:

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