Rotational Motion Quiz-11
Dear Readers,
As per analysis for previous years, it has been observed that students preparing for NEET find Physics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Biology due to their medical background. Furthermore, sections such as Physics are dominantly based on theories, laws, numerical in comparison to a section of Biology which is more of fact-based, life sciences, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced.
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Q1. Moment of inertia of a hollow cylinder of mass M and radius r about its own axis is?
Solution
Moment of inertia of a hollow cylinder of mass M and radius r about its own axis is Mr2
Moment of inertia of a hollow cylinder of mass M and radius r about its own axis is Mr2
Q2. A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach other end. During the journey of the insect, the angular speed of the disc?
Solution
From angular momentum conservation about vertical axis passing through centre. When insect is coming from circumference to centre. Moment of inertia first decrease then increase. So angular velocity increase then decrease
From angular momentum conservation about vertical axis passing through centre. When insect is coming from circumference to centre. Moment of inertia first decrease then increase. So angular velocity increase then decrease
Q3. The vector product of the force (F) and distance (r) from the centre of action represents?
Solution
Torque is a measure of how much a force acting on an object causes that object to rotate. The object rotates about an axis (O). The distance from O is r, where forces acts, hence torque Ï„=F×r. It is a vector quantity and points from axis of rotation to the point where the force acts
Torque is a measure of how much a force acting on an object causes that object to rotate. The object rotates about an axis (O). The distance from O is r, where forces acts, hence torque Ï„=F×r. It is a vector quantity and points from axis of rotation to the point where the force acts
Q4. One circular ring and one circular disc, both are having the same mass and radius. The ratio of their moments of inertia about the axes passing through their centres and perpendicular to their planes, will be?
Solution
IRing/IDisc =(MR2)/(1/2MR2 )=2:1
IRing/IDisc =(MR2)/(1/2MR2 )=2:1
Q5. When two bodies collide elastically, the force of interaction between them is?
Solution
When non-conservative force acts on a body, then mechanical energy is converted into non-mechanical energy and vice-versa.
When non-conservative force acts on a body, then mechanical energy is converted into non-mechanical energy and vice-versa.
Q6. A metre stick of mass 400 g is pivoted at one end and displaced through an angle 60°. The increase in its potential energy is?
Solution
Centre of mass of a stick lies at the mid point and when the stick is displaced through an angle 60° it rises upto height 'h' from the initial position
From the figure h=l/2-l/2 cosθ=l/2(1-cosθ) Hence the increment in potential energy of the stick =mgh=mg l/2 (1-cosθ )=0.4×10×1/2 (1-cos60° )=1J
Centre of mass of a stick lies at the mid point and when the stick is displaced through an angle 60° it rises upto height 'h' from the initial position
From the figure h=l/2-l/2 cosθ=l/2(1-cosθ) Hence the increment in potential energy of the stick =mgh=mg l/2 (1-cosθ )=0.4×10×1/2 (1-cos60° )=1J
Q7. The distance of the centre of mass of the T-shaped plate from O is?
Solution
Co-ordinate of CM is given by XCM=(m1 x1+m2 x2)/(m1+m2 )
Taking parts A and B as two bodies of same system m1=l×b×σ=8×2×σ=16σ m2=l×b×σ=6×2×σ=12σ Choosing O as origin, x1=1 m,x2=2+3=5 m ∴XCM=(16σ×1+12σ×5)/(16σ+12σ)=19/7 =2.7 m from O
Co-ordinate of CM is given by XCM=(m1 x1+m2 x2)/(m1+m2 )
Taking parts A and B as two bodies of same system m1=l×b×σ=8×2×σ=16σ m2=l×b×σ=6×2×σ=12σ Choosing O as origin, x1=1 m,x2=2+3=5 m ∴XCM=(16σ×1+12σ×5)/(16σ+12σ)=19/7 =2.7 m from O
Q8. A torque of 50 Nm acting on a wheel at rest rotates it through 200 radians in 5 sec. Calculate the angular acceleration produced?
Solution
θ=ω0 t+1/2 αt2⇒200=1/2 α(5)2⇒α=16rad/s2
θ=ω0 t+1/2 αt2⇒200=1/2 α(5)2⇒α=16rad/s2
Q9. An isolated particle of mass m is moving in a horizontal plane (x-y), along the x-axis, at a certain height above the ground. It suddenly explodes into two fragments of masses m/4 and 3m/4. An instant later, the smaller fragment is at y=+15 cm. The larger fragment at the instant is at?
Solution
Since there is no external force acting on the particle, Hence yCM=(m1 y1+m2 y2)/(m1+m2 )=0, hence (m/4)×(+15)+(3m/4)(y2 )=0⇒y2=-5 cm
Since there is no external force acting on the particle, Hence yCM=(m1 y1+m2 y2)/(m1+m2 )=0, hence (m/4)×(+15)+(3m/4)(y2 )=0⇒y2=-5 cm
Q10. The principle of conservation of angular momentum, states that angular momentum?
Solution
Remains conserved until the torque acting on it remain zero
Remains conserved until the torque acting on it remain zero
