https://file.aiquickdraw.com/mathbot/file/1726075555106is7tzf13.jpg

The question in the image is in Bengali and translates as follows:

**Question:**
"A wheel has a moment of inertia of \( 10 \, \text{kg} \cdot \text{m}^2 \). How much torque is needed to produce an angular acceleration of \( 10 \, \text{rads}^{-2} \)?"

We are given:
- Moment of inertia, \( I = 10 \, \text{kg} \cdot \text{m}^2 \)
- Angular acceleration, \( \alpha = 10 \, \text{rads}^{-2} \)

Using the formula for torque:
\[
\tau = I \cdot \alpha
\]

Substituting the values:
\[
\tau = 10 \, \text{kg} \cdot \text{m}^2 \times 10 \, \text{rads}^{-2} = 100 \, \text{Nm}
\]

Thus, the required torque is \( \boxed{100 \, \text{Nm}} \), which corresponds to option **D**.

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Would you like more details or have any other questions?

Here are 5 related questions for further practice:
1. What is the relationship between torque and angular acceleration?
2. How does moment of inertia affect the rotational motion of a body?
3. What are the SI units of moment of inertia and angular acceleration?
4. How does the distribution of mass affect the moment of inertia of a rotating object?
5. If the angular acceleration was halved, what would be the required torque?

**Tip:** Moment of inertia depends not just on the mass but also on how that mass is distributed relative to the axis of rotation.

একটি চাকার জড়তার ভামক 10 kgm² । চাকারটিতে 10 rads⁻² কৌণিক ত্বরণ সৃষ্টি করতে কত টর্ক প্রয়োগ করতে হবে?

Learn how to calculate the torque required to produce an angular acceleration of 10 rads⁻² for a wheel with a moment of inertia of 10 kgm². This problem covers key physics concepts such as torque, moment of inertia, and angular acceleration. Suitable for Grades 9-12.

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