Momentum will be conserved in one dimension in the explosion.
<span>
Given that the fragment a acquires three
times the kinetic energy of the fragment b.
<span>
P</span><span><span>initial </span><span>= p</span></span>final ⇒ 0 =mₐv⁰ₐ+mьv⁰ь= 0 ⇒ v⁰ь = -mₐv⁰ₐ/mь
KE= 3KEь
⇒1/2 mₐv⁰ₐ² = 3 (1/2mьv⁰ь²)
</span><span>
⇒1/2 mₐv⁰ₐ² = 3/2 mь(-mₐv⁰ₐ/mь)²
⇒1/2 mₐv⁰ₐ² = 3/2 mь(mₐ²v⁰ₐ²/mь²)
</span>
⇒1/2 x 2/3 = mₐ/mь= 1/3
<span>
<span>
Thus the ratio
of the masses of the fragments is 1:3.
</span></span>
Explanation:
d = Diameter of wheel = 27 cm
r = Radius = 
m = Mass of wheel = 800 g
= Initial angular velocity = 
Equation of rotational motion

Moment of inertia is given by

Torque is given by

The torque the friction exerts is -0.0037406448 Nm
For more information on torque and moment of inertia refer
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The mass of the kid and the sled is 50.0 kg
Explanation:
The sled starts to move when the force applied becomes larger than the maximum force of static friction, which is given by

where
is the coefficient of static friction
m is the mass of the kid + the sled
is the acceleration of gravity
Here the sled starts moving when the force applied is 61.2 N, so

And we also know

Therefore, we can find the mass of the kid and the sled by re-arranging the equation:

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