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51.

Two cylinders having radii `2R` and `R` and moment of inertia `4I` and `I` about their central axes are supported by axles perpendicular to their planes. The large cylinder is initially rotating clockwise with angular velocity `omega_(0)`. The small cylinder is moved to the right until it touches the large cylinder and is caused to rotate by the frictional force between the two. Eventually slipping ceases and the two cylinders rotate at constant rates in opposite directions. During this A. angular moment of system is conservedB. kinetic energy is conservedC. neither the angular momentum nor the kinetic energy is conservedD. both the angular momentum and kinetic energy are conserved

Answer» Correct Answer - C
Discussion
52.

Two discs `A` and `B` are mounted coaxially ona vertical axle. The discs have moments of inertia `l` and `2l` respectively about the common axis. Disc A is imparted an initial angular velocity `2 omega` using the centre potential energy of a spring compressed by a distance `x_(1)`. Disc `B` is imparted angular velocity `omega` by a spring having the same spring constant and compressed by a distance `x_(2)`. Both the disc rotate in the clockwise direction. The loss of kinetic energy the above process is -A. `(Iomega^(2))/2`B. `(Iomega^(2))/3`C. `(Iomega^(3))/4`D. `(Iomega^(3))/6`

Answer» Correct Answer - B
Discussion
53.

A spol is lying on a rough horizontal surface. Forces `F_(1),F_(2),F_(3)` and `F_(4)` act in different directions, as represented in column I. Match the information in column I with II.

Answer» Correct Answer - A::B::C::D
Discussion
54.

Two moving particles `P` and `Q` are 10cm apart at any instant. Velocity of P is `8 m//s` at `30^(@)`, from line joining the P and Q and velocity of Q is `6m//s` at `30^(@)`. Calculate the angular velocity of P w.r.t. Q A. `0rad//s`B. `0.1 rad//s`C. `0.4rad//s`D. `0.7rad//s`

Answer» Correct Answer - D
Discussion
55.

A sphere `S` rolls without slipping moving with a constant speed on a plank `P`. The friction between the upper surface of `P` and the sphere is sufficient to prevent slipping, while the lower surface of `P` is smooth and rest on the ground. Initially `P` is fixed on the ground by a pin `N`. If `N` is suddenly removed A. `S` will begin to slip on `P`B. `P` will begin to move backwardsC. The speed of `S` will decrease and its angular velocity with increaseD. There will be no change in the motion of `S` and `P` will still be in rest

Answer» Correct Answer - D
Discussion
56.

A wheel of radius `R` rolls without slipping on a horizontal ground. The distance travelled by a point on the rim in one complete rotation is:A. `2piR`B. `8R`C. `2R`D. `piR`

Answer» Correct Answer - B
Discussion
57.

A ring mass `m` and radius `R` has three particle attached to the ring as shown in the figure. The centre of the centre `v_(0)`. Find the kinetic energy of the system. (Slipping is absent). .A. `6mv_(0)^(2)`B. `12mv_(0)^(2)`C. `2mv_(0)^(2)`D. `8mv_(0)^(2)`

Answer» Correct Answer - A
Discussion
58.

Four point masses, each of value `m`, are placed at the corners of square `ABCD` of side `l`. The moment of inertia of this system about an axis passing through `A` and parallel to `BD` is -A. `3ml^(2)`B. `ml^(2)`C. `2ml^(2)`D. `sqrt(3)ml^(2)`

Answer» Correct Answer - A
Discussion
59.

A wire of length `l` and mass `m` is first bent in a circle, then in a square and then in an equilateral triangle. The moment of inertia in these three cases about an axis perpendicular to their planes and passig through their centres of mass are `I_(1),I_(2)` & `I_(3)` respectively. Then maximum of them is:A. `I_(1)`B. `I_(2)`C. `I_(3)`D. data insufficient

Answer» Correct Answer - A
Discussion
60.

A wire of length `l` and mass `m` is bent in the form of a rectangle `ABCD` with `(AB)/(BC)=2`. The moment of inertia of this wife frame about the side `BC` isA. `22/252 ml^(2)`B. `8/203 ml^(2)`C. `5/136 ml^(2)`D. `7/162 ml^(2)`

Answer» Correct Answer - D
Discussion