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If the road of the previous problem is horizontal (no banking), what should be the minimum friction coefficient so that scooter going at 18 km/hr does not skid?
Concept: undefined >> undefined
A circular road of radius 50 m has the angle of banking equal to 30°. At what speed should a vehicle go on this road so that the friction is not used?
Concept: undefined >> undefined
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All the particles of a body are situated at a distance R from the origin. The distance of the centre of mass of the body from the origin is
Concept: undefined >> undefined
A body falling vertically downwards under gravity breaks in two parts of unequal masses. The centre of mass of the two parts taken together shifts horizontally towards
Concept: undefined >> undefined
A body at rest breaks into two pieces of equal masses. The parts will move
Concept: undefined >> undefined
A body has its centre of mass at the origin. the x-coordinates of the particles
(a) may be all positive
(b) may be all negative
(c) may be all non-negative
(d) may be positive for some cases and negative in other cases.
Concept: undefined >> undefined
A body moving towards a finite body at rest collides with it. It is possible that
(a) both the bodies come to rest
(b) both the bodies move after collision
(c) the moving body comes to rest and the stationary body starts moving
(d) the stationary body remains stationary, the moving body changes its velocity.
Concept: undefined >> undefined
In a head-on elastic collision of two bodies of equal masses
(a) the velocities are interchanged
(b) the speeds are interchanged
(c) the momenta are interchanged
(d) the faster body slows down and the slower body speeds up.
Concept: undefined >> undefined
A block at rest explodes into three equal parts. Two parts start moving along X and Y axes respectively with equal speeds of 10 m/s. Find the initial velocity of the third part.
Concept: undefined >> undefined
When tall building are constructed on earth, the duration of day-night slightly increases. Is it true?
Concept: undefined >> undefined
Is Archimedes' principle valid in an elevator accelerating up ? In a car accelerating on a level road?
Concept: undefined >> undefined
Why is it easier to swim in sea water than in fresh water?
Concept: undefined >> undefined
A ferry boat loaded with rocks has to pass under a bridge. The maximum height of the rocks is slightly more than the height of the bridge so that the boat just fails to pass under the bridge. Should some of the rocks be removed or some more rocks be added?
Concept: undefined >> undefined
A 20 N metal block is suspended by a spring balance. A beaker containing some water is placed on a weighing machine which reads 40 N. The spring balance is now lowered so that the block gets immersed in the water. The spring balance now reads 16 N. The reading of the weighing machine will be
Concept: undefined >> undefined
A body of mass m makes an elastic collision with another identical body at rest. Show that if the collision is not head-on the bodies go at right angle to each other after the collision.
Concept: undefined >> undefined
A small particle travelling with a velocity v collides elastically with a spherical body of equal mass and of radius r initially kept at rest. The centre of this spherical body is located a distance ρ(< r) away from the direction of motion of the particle (see figure below). Find the final velocities of the two particles.
[Hint : The force acts along the normal to the sphere
through the contact. Treat the collision as onedimensional
for this direction. In the tangential direction no force acts and the velocities do not change].
Concept: undefined >> undefined
Figure shows a small body of mass m placed over a larger mass M whose surface is horizontal near the smaller mass and gradually curves to become vertical. The smaller mass is pushed on the longer one at a speed v and the system is left to itself. Assume that all the surface are frictionless. (a) Find the speed of the larger block when the smaller block is sliding on the vertical part. (b) Find the speed of the smaller mass when it breaks off the larger mass at height h. (c) Find the maximum height (from the ground) that the smaller mass ascends. (d) Show that the smaller mass will again land on the bigger one. Find the distance traversed by the bigger block during the time when the smaller block was in its flight under gravity.
Concept: undefined >> undefined
A metal cube is placed in an empty vessel. When water is filled in the vessel so that the cube is completely immersed in the water, the force on the bottom of the vessel in contact with the cube
Concept: undefined >> undefined
A solid floats in a liquid in a partially dipped position.
(a) The solid exerts a force equal to its weight on the liquid.
(b) The liquid exerts a force of buoyancy on the solid which is equal to the weight of the solid.
(c) The weight of the displaced liquid equals the weight of the solid.
(d) The weight of the dipped part of the solid is equal to the weight of the displaced liquid.
Concept: undefined >> undefined
A solid is completely immersed in a liquid. The force exerted by the liquid on the solid will
(a) increase if it is pushed deeper inside the liquid
(b) change if its orientation is changed
(c) decrease if it is taken partially out of the liquid
(d) be in the vertically upward direction.
Concept: undefined >> undefined
