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Motion in a Straight Line — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Straight Line1 Mark
MCQ
A spring with one end attached to a mass and the other to a rigid support is stretched and released.
  • A
    Magnitude of acceleration, when just released is maximum.
  • B
    Magnitude of acceleration, when at equilibrium position, is maximum.
  • C
    Speed is maximum when mass is at equilibrium position.
  • ✓
    Both $A$ and $C$
✓

Answer

Correct option: D.
Both $A$ and $C$

As shown in the figure above when spring is stretched by length $x,$ restoring force will be $F = -kx (-ve$ sigh shows that the force is always is the direction opposite to displacement $x).$ Then the potential energy of the stretched spring.
$=\text{PE}=\frac{1}{2}\text{kx}^2$
The restoring force is central, hence when particle is released it will execute Simple Harmonic Motion about equilibrium position.
Acceleration will be $\text{a}=\frac{\text{F}}{\text{m}}=\frac{\text{-kx}}{\text{m}}$
At equilibrium position, $\text{x}=0\Rightarrow\text{a}=0$
Hence, when just released $\text{x}=\text{x}_\text{max}$
Hence, acceleration is maximum. Thus option $(a)$ is correct.
At equilibrium whole $PE$ will be converted to $KE,$
so $KE$ will be maximum and hence, speed will be maximum. Thus option $(c)$ is correct.

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