An object of mass \(3\,\text{kg}\) is tied by a string of negligible mass to a ceiling and held such that the string is taut. The object is released suddenly such that the string remains taut. Its acceleration when released is \((g=10\,\text{m/s}^2)\):
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For a pendulum released from rest, the initial acceleration is tangential and equal to
\[
g\sin\theta.
\]
There is no centripetal acceleration at the instant of release because initial speed is zero.
Step 1: Describe the physical setup.
A 3 kg object is tied to a string and held at an angle of $30^\circ$ from the vertical (as shown by the figure's intent). When released, it swings like a pendulum.
Step 2: Identify the forces at the moment of release.
At the instant of release, the object is momentarily at rest.
Two forces act: weight $mg$ (downward) and string tension $T$ (along the string toward the pivot).
Step 3: Understand why only tangential acceleration matters at release.
The centripetal acceleration = $v^2/l$. Since velocity is zero at release, centripetal acceleration = 0.
So the total acceleration at that instant equals the tangential acceleration only.
Step 4: Resolve gravity along the tangential direction.
The tangential direction is perpendicular to the string. The component of gravity tangential to the circular path is:
\[
F_\text{tangential} = mg\sin\theta
\]
where $\theta = 30^\circ$ is the angle the string makes with the vertical.
Step 5: Apply Newton's second law in the tangential direction.
\[
ma_t = mg\sin 30^\circ
\]
\[
a_t = g\sin 30^\circ = 9.8 \times 0.5 = 4.9\,\text{m/s}^2
\]
Step 6: State the answer.
Using $g = 9.8\,\text{m/s}^2$ (standard value) gives exactly:
\[
\boxed{4.9\,\text{m/s}^2}
\]
