Question
A block of mass $m$ is connected to three springs, each of spring constant $k$ as shown in Fig. $1.26 .$ The block is pulled by $x$ in the direction of $C$. Find resultant spring constant.(A) $k$(B) $2 k$(C) $3 \mathrm{k}$(D) $\frac{3 k}{2}$
Step 1
This gives us the net force as $F_{net} = -kx$ for spring C and $-kx cos60°$ for each of the springs A and B. Show more…
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Two blocks $A$ and $B$ of mass $m$ and $2 \mathrm{~m}$ respectively are connected by a massless spring of force constant $k$. They are placed on a smooth horizontal plane. They are stretched by an amount $x$ and then released. The relative velocity of the blocks when the spring comes to its natural length is (A) $x \sqrt{\frac{3 k}{2 m}}$ (B) $x \sqrt{\frac{2 k}{3 m}}$ (C) $x \sqrt{\frac{2 k}{m}}$ (D) $x \sqrt{\frac{3 k}{m}}$
System shown in figure is in equilibrium. Find the magnitude of net change in the string tension between two masses just after, when one of the springs is cut. Mass of both the blocks is same and equal to $m$ and spring constant of both spring is $k$ (a) $\frac{m g}{2}$ (b) $\frac{m g}{4}$ (c) $\frac{3 m g}{4}$ (d) $\frac{3 m y}{2}$
Laws of Motion and Friction
Section B
In the adjoining Fig. $5.36$ block $A$ is of mass $m$ and block $B$ is of mass $2 m .$ The spring has a force constant $k$. All the surfaces are smooth and the system is released from rest with the spring not being stretched (A) The maximum extension of the spring is $\frac{4 m g}{k}$ (B) The speed of block $A$ when extension in spring is $\frac{2 m g}{k}$, is $2 g \sqrt{\frac{2 m}{3 k}}$ (C) Net acceleration of block $B$ when the extension in the spring is maximum, is $\frac{2}{3} g$. (D) Tension in the thread for extension of $\frac{2 m g}{k}$ in spring is $m g$.
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