Multiple Choice QuestionsA body weighed 250 N on the surface assuming the earth to be a sphere of uniform mass density, how much would it weigh halfway down to the centre of the earth?
195 N
240 N
125 N
210 N
C.
125 N
At a depth 'd' below the surface of the earth.
mg' =
M' =
⇒ g' =
g' =
On the surface of the earth
g =
g =
∴ g' =
∴ The body weighed 250 N on the surface of the earth would weigh × 250 = 125 N, halfway down towards the centre of the earth.
Assertion: Centripetal force does no work.
Reason: Force and displacement are perpendicular to each other.
If both assertion and reason are true and reason is the correct explanation of assertion.
If both assertion and reason are true but reason is not the correct explanation of assertion.
If assertion is true but reason is false.
If assertion is false but reason is true.
A.
If both assertion and reason are true and reason is the correct explanation of assertion.
Since centripetal force is perpendicular to the displacement of the body, work done is zero.
W = = Fd cosθ
The kinetic energy of a body becomes four times its initial value. The new linear momentum will be
same as the initial value
four times the initial value
twice of the initial value
eight times of the initial value
C.
twice of the initial value
Initial kinetic energy ( E1) = E
and final kinetic energy (E2 ) = 4E
The kinetic energy of a body =
Since the value of m remains constant
Therefore for the kinetic energy to be 4 times, the new value velocity (v) should be 2 times the initial value
Initial linear momentum
(p1) = mv
Therefore new linear momentum
(p2) = m × 2v
= 2mv
(p2) = 2p1
Maximum energy transfer for an elastic collision will occur if one body is at rest when
m1 = m2
m2 = m1
m1 >> m2
m2 >> m1
A.
m1 = m2
During elastic collision between two equal masses, the velocity of the two bodies get interchanged. So if one body is at rest, energy transfer will be maximum
for m1 = m2.
A car and a container, moving with equal kinetic energies are stopped by applying a negative acceleration. Then
container will move less distance before being stopped
both will become stationary after moving some distance
car will move less distance before being stopped
none of the above
C.
car will move less distance before being stopped
Since, a car and a container have equal kinetic energies, the velocity of car will be greater and when same retarded force is applied to both, the car will move less distance, because retardation will be more on car
n balls each of mass m and velocity v collide with a wall, assume that the collisions are perfectly elastic. The pressure exerted per second on the wall is
3 mnv
mnv
2mnv
none
C.
2mnv
Pressure = change in momentum
Change in momentum for a ball = mv − (− mv) = 2mv
For n balls change in momentum = 2mnv
Which of the following is path dependent?
U
PdV
P
V
B.
PdV
Dependent on path taken to establish property or value.
PdV is the path dependent.
The momentum of two masses m1 and m2 are same. The ratio of their kinetic energies E1 and E2 is
m1 : m2
m2 : m1
m12 : m22
C.
m2 : m1
Momentum of first body = momentum of second body = mv
E =
=
Hence, =
Two particles are seen to collide and move jointly together after the collision. During such a collision, for the total system.
both the mechanical energy and the linear momentum are conserved
linear momentum is conserved but not the mechanical energy
neither the mechanical energy nor the linear momentum is conserved
mechanical energy is conserved but not the linear momentum
B.
linear momentum is conserved but not the mechanical energy
This is a case of a totally inelastic collision, in which linear momentum is conserved but the total mechanical energy is not conserved.
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