EASY
Earn 100

A body of mass 0.5 kg is whirled with a velocity of 2 m s-1 using 0.5 m length string which can withstand a tension of 15 N.  Neglecting the force of gravity on the body predict whether the string will break or not.

Important Questions on Laws of Motion

EASY
A small object placed on a rotating horizontal turn table just slips when it is placed at a distance of 4 cm from the axis of rotation, if the angular velocity of the turn-table is doubled, the object slips when its distance from the axis of rotation is
EASY
The position vector of a particle R as a function of time is given by:

R=4sin2πti^+4cos(2πt)j^

Where R is in meters, t is in seconds and i^ and j^ denote unit vectors along x- and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?
MEDIUM
One end of massless spring of spring constant 100 N/m and natural length 0.49 m is fixed and other end is connected to a body of mass 0.5 kg lying on a frictionless horizontal table. The spring remains horizontal. If the body is made to rotate at an angular velocity of 2rad/s, then the elongation of the spring will be
MEDIUM
A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that r=L2. The speed of particle will be :
EASY
One end of a string of length 'l' is connected to a particle of mass 'm' and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed 'v', the net force on the particle (directed towards the centre is: (T is the tension in the string)
MEDIUM
A disc of radius 0.4 m and mass 1 kg rotates about an axis passing through its centre and perpendicular to its plane. The angular acceleration is 10 rad/s2. The tangential force applied to the rim of the disc is
MEDIUM
If a particle of mass m is moving in a horizontal circle of radius r with a centripetal force -Kr2, total energy is
EASY

A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against the wall with a speed v. Which of the following curve represents the correct relation between the normal reaction on the block by the wall N and speed of the block v?

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MEDIUM

Two spheres of equal masses are attached to a string of length 2 m as shown in figure. The string and the sphere are then whirled in a horizontal circle about O at a constant rate. What is the value of the ratio?
Tension in the string between P and QTension in the string between P and O=?

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MEDIUM
A simple pendulum is suspended from the ceiling of a car taking a turn of radius 10 m at a speed of 10 m s-1. Find the angle made by the string of the pendulum with the vertical if this angle does not change during the turn. (Assume g=10 m s-2)
HARD
Distinguish between centripetal and centrifugal force.
MEDIUM
An insect is at the bottom of a hemispherical ditch of radius 1m. It crawls up the ditch but starts slipping after it is at height h from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then his :g=10 m s-2
HARD
A flat curve on a highway has a radius of curvature 400 m. A car goes around a curve at a speed of 32 m/s. What is the minimum value of the coefficient of friction that will prevent the car from sliding? (g = 9.8 m/s2)
EASY
A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to R3. Its time period of revolution will be given by :
MEDIUM
A spherical bob hangs from a light inextensible string and moves in a horizontal circle with string making angle θ with the vertical. The length l of the string is then very slowly increased so that the motion is circular at all times to a good approximation. If h is the height from center of the circle to the pivot and r is the radius of the circle then hra. The value of a is
HARD
A smooth wire of length 2πr is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed ω about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of ω2 is equal to:
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EASY
A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m s-1. A bob is suspended from the roof of the car by a light wire of length 1.0 m. The angle made by the wire with the vertical is (in radian)
MEDIUM
A ball of mass m is attached to the free end of an inextensible string of length l. Let T be the tension in the string. The ball is moving in horizontal circular path about the vertical axis. The angular velocity of the ball at any particular instant will be
MEDIUM
A pulley of radius 2 m is rotated about its axis by a force =20t-5t2 newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2, the number of rotation made by the pulley before its direction of motion is reversed is
MEDIUM
A conical pendulum of length l makes an angle θ=45° with respect to Z-axis and moves in a circle in the XY plane. The radius of the circle is 0.4 m and its center is vertically below O. The speed of the pendulum, in its circular path, will be - Take g=10 m s-2
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