Answer:
1.8 x 10⁻³⁴ m.
Explanation:
de Broglie wavelength ( λ ) of a moving particle is given by the following expression
λ = h / momentum of the particle
In other words, de Broglie wavelength depends upon the momentum of the particle.
In the given case , particle A which is stationary collides with another particle B having some momentum . After the collision , they move together.No external force acts on them . Therefore after the collision , their momentum will be conserved. In other words , their momentum remains the same as earlier. So their de Broglie wave length will also be the same as earlier , since it depends on the momentum of the moving body.
Hence the de Broglie wavelength of the object will be 1.8 x 10⁻³⁴ m.
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(a) 24.6 Nm
The torque produced by the net thrust about the center of the circle is given by:
where
F is the magnitude of the thrust
r is the radius of the wire
Here we have
F = 0.795 N
r = 30.9 m
Therefore, the torque produced is
(b) 
The equivalent of Newton's second law for a rotational motion is
where
is the torque
I is the moment of inertia
is the angular acceleration
If we consider the airplane as a point mass with mass m = 0.741 kg, then its moment of inertia is
And so we can solve the previous equation to find the angular acceleration:
(c) 
The linear acceleration (tangential acceleration) in a rotational motion is given by
where in this problem we have
is the angular acceleration
r = 30.9 m is the radius
Substituting the values, we find
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Answer:
10.2 m .
Explanation:
Let object falls by angle θ .
At any moment after the fall , there are two forces acting on the sphere
1 ) mg cosθ which is a component of weight towards the centre 2 ) normal reaction of the surface R .
mgcosθ - R is net force acting, which provides centripetal force
mgcosθ - R = mv² / r
But v² = 2g r( 1-cosθ ) [ object falls by height ( r - r cosθ ).
mgcosθ - R = m / r x 2g r( 1-cosθ )
When the object is no longer in touch with sphere,
R = 0
mgcosθ = m / r x 2g r( 1-cosθ )
3 gr cosθ = 2gr
cosθ = 2/3
height of fall
= r ( 1-cosθ )
r ( 1 - 2/3 )
1/3 r
1/3 x 15.3
5.1 m
Height from the ground
15.3 - 5.1
10.2 m .
