Physics Test

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Physics Test - 19

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Question 1
1 / -0

Two balls marked 1 and 2 of the same mass m and a third ball marked 3 of mass M are arranged over a smooth horizontal surface as shown in the figure. Ball 1 moves with a velocity v₁toward balls 2 and 3. All collisions are assumed to be elastic. If M < m, the number of collisions between the balls will be

A
one

B
two

C
three

D
four

Solution
Question 2
1 / -0

A body of mass m₁ moving at a constant speed undergoes an elastic collision with a body of mass m₂initially at rest. The ratio of the kinetic energy of mass m₁ after the collision to that before the collision is

A

B

C

D

Solution
Question 3
1 / -0

If two balls each of mass 0.06 kg moving in opposite directions with speed of 4 ms^-1 collide and rebound with same speed, then the impulse imparted to each ball due to other is

A
0.48 kg ms^-1

B
0.53 kg ms^-1

C
0.81 kg ms^-1

D
0.92 kg ms^-1

Solution

Impulse = (0.06 x 4 + 0.06 x 4) x 1 = 0.48 kg m/s
Question 4
1 / -0

A boy, while catching a ball, experiences an impulse of 6 Ns. If the mass of the ball is 200 g, then what was the speed of the ball before it was caught?

A
10 ms^-1

B
30 ms^-1

C
20 ms^-1

D
40 ms^-1

Solution
Question 5
1 / -0

A 1 kg ball moving at 12 m/s collides head-on with a 2 kg ball moving in the opposite direction at 24 m/s. What is the velocity of each ball after the impact, if the coefficient of restitution is 2/3 ?

A
v₁ = -28 m/s, v₂ = -4 m/s

B
v₁ = 20 m/s, v₂= 2 m/s

C
v₁ = -30 m/s, v₂= -18 m/s

D
v₁ = -20 m/s, v₂= -4 m/s

Solution
Question 6
1 / -0

A cord is wound around the circumference of a bicycle wheel (without tyre) of diameter 1 m. A mass of 2 kg is tied to the end of the cord and it is allowed to fall from rest. The weight falls 2 m in 4 s. The axle of the wheel is horizontal and the wheel rotates with its plane vertical. The angular acceleration produced is (Take g = 10 ms^–2)

A
0.5 rad s^–2

B
1.0 rad s^–2

C
2.0 rad s^–2

D
4.0 rad s^–2

Solution
Question 7
1 / -0

The track shown in the figure ends in a circular track of radius r with centre at O. A small solid sphere of mass m rolls from rest without slipping from a point A at a height h = 6r from the level ground. What is the speed of the sphere when it reaches a point B at height r above the level ground?

A
√(10gr)

B
√(50/7gr)

C
√(22/7gr)

D
Zero

Solution
Question 8
1 / -0

In the rectangular lamina ABCD shown in the figure below, a = AB = BC/2. The moment of inertia of the lamina is minimum along the axis passing through

A
BC

B
AB

C
HF

D
EG

Solution
Question 9
1 / -0

Three particles, each of mass 'm' g, are situated at the vertices of an equilateral triangle ABC of side l cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB in the plane of ABC in gram-cm² unit will be

A
(3/4) ml²

B
2 ml²

C
(5/4) ml²

D
(3/2) ml²

Solution
Question 10
1 / -0

A thin uniform metallic triangular sheet of mass M has sides AB = BC = L as shown in the figure. What is its moment of inertia about axis AC lying in the plane of the sheet?

A
ML²/12

B
ML²/6

C
ML²/3

D
2ML²/3

Solution
Question 11
1 / -0

The Young's modulus of the material of a wire is 2 x 10¹⁰ Nm^–2. If the elongation strain is 1%, then the energy stored in the wire per unit volume (in Jm^–3) is

A
10⁶

B
10⁸

C
2 x 10⁶

D
2 x 10⁸

Solution
Question 12
1 / -0

A spring of force constant k is cut into two equal halves. The force constant of each half is

A
k/√2

B
k/2

C
k

D
2k

Solution
Question 13
1 / -0

A spring of force constant k is cut into two pieces such that one piece is double the length of the other. The force constant of the longer piece will be

A
1.5k

B
3k

C
2k

D
2/3k

Solution
Question 14
1 / -0

A hollow metallic sphere, filled with water, is hung from a support by a long thread. A small hole is made at the bottom of the sphere and it is oscillated. How will the time period of oscillations be affected as water slowly flows out of the hole?

A
The time period will remain unchanged as water is flowing out.

B
The time period will keep increasing until the sphere is empty.

C
The time period will keep decreasing until the sphere is empty.

D
The time period will increase at first then decrease untill the sphere is empty; finally the period will be the same as that when the sphere was full of water.

Solution

The length of the pendulum (I) is the distance between the point of support and the centre of mass of the sphere. The centre of mass (CM) of a sphere is at its centre when it is empty and completely filled with water. The CM falls below the centre of the sphere as the water flows out until the mass of the water becomes same as the mass of the sphere after which CM will shift upward and the CM will return to its original value . Hence, the effective length of the pendulum (and hence, its time period) will increase then decreases and when sphere is empty then it becomes equal to the time period when the sphere was full of water. Thus, the correct choice is (4).
Question 15
1 / -0

A particle in SHM is described by the displacement equation x(t) = A cos (ωt + θ). If the initial (t = 0) position of the particle is 1 cm and its initial velocity is π cm/s, then what is its amplitude? (The angular frequency of the particle is πs^-1.)

A
1 cm

B
√2 cm

C
2 cm

D
2.5 cm

Solution