Question:
As shown in the figure, an iron block \(A\) of volume \(0.25\;m^3\) is attached to a spring \(S\) of unstretched length \(1.0\;m\) and hanging to the ceiling of a roof. The spring gets stretched by \(0.2\;m\). This block is removed and another block \(B\) of iron of volume \(0.75\;m^3\) is now attached to the same spring and kept on a frictionless inclined plane of \(30^\circ\) inclination. The distance of the block from the top along the incline at equilibrium is
As shown in the figure, an iron block \(A\) of volume \(0.25\;m^3\) is attached to a spring \(S\) of unstretched length \(1.0\;m\) and hanging to the ceiling of a roof. The spring gets stretched by \(0.2\;m\). This block is removed and another block \(B\) of iron of volume \(0.75\;m^3\) is now attached to the same spring and kept on a frictionless inclined plane of \(30^\circ\) inclination. The distance of the block from the top along the incline at equilibrium is
Show Hint
For a block attached to a spring on a smooth inclined plane, balance the spring force with the component of weight along the plane:
\[
kx=mg\sin\theta
\]
Updated On: Jun 22, 2026
- \(1.1\;m\)
- \(1.3\;m\)
- \(1.6\;m\)
- \(1.9\;m\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Use the first case to find spring constant relation.
For block \(A\), volume is \[ V_A=0.25\;m^3 \] Let density of iron be \(\rho\).
Mass of block \(A\) is \[ m_A=\rho V_A=0.25\rho \] The spring stretches by \[ x_A=0.2\;m \] At equilibrium, \[ kx_A=m_Ag \] \[ k(0.2)=0.25\rho g \]
Step 2: Use the second case on inclined plane.
For block \(B\), \[ V_B=0.75\;m^3 \] So, \[ m_B=0.75\rho \] On a smooth inclined plane of angle \(30^\circ\), the component of weight along the plane is \[ m_Bg\sin30^\circ \] At equilibrium, \[ kx_B=m_Bg\sin30^\circ \] \[ kx_B=0.75\rho g\cdot \frac12 \] \[ kx_B=0.375\rho g \]
Step 3: Find the extension of the spring.
From the first case, \[ k(0.2)=0.25\rho g \] So, \[ k=\frac{0.25\rho g}{0.2} \] Now, \[ x_B=\frac{0.375\rho g}{k} \] Substitute the value of \(k\): \[ x_B= \frac{0.375\rho g}{\frac{0.25\rho g}{0.2}} \] \[ x_B=\frac{0.375\times 0.2}{0.25} \] \[ x_B=0.3\;m \]
Step 4: Find the distance from the top along the incline.
Unstretched length of the spring is \[ 1.0\;m \] Extension is \[ 0.3\;m \] Therefore, distance of the block from the top along the incline is \[ 1.0+0.3=1.3\;m \]
Step 5: Final conclusion.
Hence, the required distance is \[ \boxed{1.3\;m} \]
For block \(A\), volume is \[ V_A=0.25\;m^3 \] Let density of iron be \(\rho\).
Mass of block \(A\) is \[ m_A=\rho V_A=0.25\rho \] The spring stretches by \[ x_A=0.2\;m \] At equilibrium, \[ kx_A=m_Ag \] \[ k(0.2)=0.25\rho g \]
Step 2: Use the second case on inclined plane.
For block \(B\), \[ V_B=0.75\;m^3 \] So, \[ m_B=0.75\rho \] On a smooth inclined plane of angle \(30^\circ\), the component of weight along the plane is \[ m_Bg\sin30^\circ \] At equilibrium, \[ kx_B=m_Bg\sin30^\circ \] \[ kx_B=0.75\rho g\cdot \frac12 \] \[ kx_B=0.375\rho g \]
Step 3: Find the extension of the spring.
From the first case, \[ k(0.2)=0.25\rho g \] So, \[ k=\frac{0.25\rho g}{0.2} \] Now, \[ x_B=\frac{0.375\rho g}{k} \] Substitute the value of \(k\): \[ x_B= \frac{0.375\rho g}{\frac{0.25\rho g}{0.2}} \] \[ x_B=\frac{0.375\times 0.2}{0.25} \] \[ x_B=0.3\;m \]
Step 4: Find the distance from the top along the incline.
Unstretched length of the spring is \[ 1.0\;m \] Extension is \[ 0.3\;m \] Therefore, distance of the block from the top along the incline is \[ 1.0+0.3=1.3\;m \]
Step 5: Final conclusion.
Hence, the required distance is \[ \boxed{1.3\;m} \]
Was this answer helpful?
0
0
Top AP EAPCET Physics Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The radii of the two columns in a U - tube are r1 and r2. When a liquid of density p (angle of contact is $ 0{}^\circ $ ) is filled in it, the level difference of the liquid in the two arms is h. The surface tension of the liquid is: (g = acceleration due to gravity)
- A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is
View More Questions
Top AP EAPCET Hooke's Law Questions
A 4 kg mass is suspended as shown in the figure. All pulleys are frictionless and spring constant \( K \) is \( 8 \times 10^3 \) Nm\(^{-1}\). The extension in spring is ( \( g = 10 \) ms\(^{-2}\) )
A 3 kg block is connected as shown in the figure. Spring constants of two springs \( K_1 \) and \( K_2 \) are 50 Nm\(^{-1}\) and 150 Nm\(^{-1}\) respectively. The block is released from rest with the springs unstretched. The acceleration of the block in its lowest position is ( \( g = 10 \) ms\(^{-2}\) )
- Two springs A and B fixed at the top and are stretched by 8 cm and 16 cm respectively, when loads of 20 N and 10 N are suspended at the lower ends. The ratio of the spring constants of the springs A and B is:
- The ratio of the stress to the strain within the elastic limit is called
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions