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Solved examples
Question 1. A body fall from height H.if t1 is time taken for covering first half height and
t2 be time taken for second half.Which of these relation is true for t1 and t2
a. t1 > t2
b. t1 < t2
c t1=t2
d Depends on the mass of the body
Question 2 .A 1 kg ball moving at 12 m/s collides head on with 2 kg ball moving with 24 m/s in opposite direction.What are the velocities after collision if e=2/3?
a. v1=-28 m/s,v2=-4 m/s
b. v1=-4 m/s,v2=-28 m/s
c. v1=28 m/s,v2=4 m/s
d. v1=4 m/s,v2=28 m/s
Question 3.A system consisting of two objects has a total momentum of (18 kgm/sec)i and its center of mass has the velocity of (3 m/s)i.One of the object has the mass 4 kg and velocity (1.5 m/s)i.The mass and velocity of the other objects are
a. 2 kg, (6 m/s)i
b. 2 kg, (-6 m/s)i
c. 2 kg, (3 m/s)i
d. 2 kg, (-3 m/s)i
Question 4.A moving bullet hits a solid target resting on a frictionless surface and get embeded in it.What is conserved in it?
a. Momentum Alone
b KE alone
c. Both Momentum and KE
d. Neither KE nor momentum
Question 5. A stationary body of mass 3 kg explodes into three equal parts.Two of the pieces fly off at right angles to each other with the velocities 2i m/s and 3j m/s.If the explosion takes place in 10-3 sec.find out the average force action on the third piece in N
a.(-2i-3j)103
b. (2i+3j)103
c (2i-3j)10-3
d. none of these
Question 6.A bullet of mass m is fired horizontally with a velocity u on a wooden block of Mass M suspended from a support and get embeded into it.The KE of th wooden + block system after the collisson
a.m2u2/2(M+m)
b.mu2/2
c. (m+M)u2/2
d. mMu2/2(M+m)
Question 7.A body of Mass M and having momentum p is moving on rough horizontal surface.If it is stopped in distance s.Find the value of coefficient of friction
a.p2/2M2gs
b. p/2Mgs
c. p2/2Mgs
d. p/2M2gs
Question 8. Which of these is true of a conservative force?
a. Workdone between two points is independent of the path
b. Workdone in a closed loop is zero
c. if the workdone by the conservative is positive,its potential energy increases
d. None of the these
Question 9. A simple pendulum consists of a mass attached to a light string l. if the system is oscillating through small angles which of the following is true
a.The freqiency is independent of the acceleration due to gravity g
b.The period depends on the amplitude of the ocsillation
c.the period is independent of mass m
d. the period is independent of lenght l
Question 10. A body of mass m is dropped from a certain height.it has velocity v1 when it is at a height h1 above the ground.it has velocity v2 when it is at a height h2 above the ground.which of the following is true
a.v12-v22=2g(h1-h2)
b.v12-v22=2g(h2-h1)
c. v1-v2=√2g(√h2-√h1)
d. v1-v2=√2g(√h1-√h2)
Question 11.A pendulum has a length l.Its bob is pulled aside from its equilibrium position through any angle θ and then released.The speed of the bob when its passes through it equalibrium position
a.&radic:2gl
b. &radic:2gl(1-cosθ)
c.&radic:2glcosθ
d.&radic:2gl(1-sinθ
Question 12.A rockets works on the principle of conservation of
a. Linear momentum
b.mass
c.energy
d. angular momentum
Question 13.A flat car of weight W roll without resistance along on a horizontal track .Intially the car together with weight w is moving to the right with speed v.What invcrement of the velocity car will obtain if man runs with speed u reltaive to the floor of the car and jumps of at the left?
a.wu/w+W
b. Wu/W+w
c. (W+w)u/w
d. none of the above
Question 14.A delivery boy wishes to launch a 2.0 kg package up an inclined plane with sufficent speed to reach the top of the incline.The plane is 3 mlong and is inclined at 20.Coefficent of friction between the package and the inclined plane is .40. what minimum intial KE must the boy suply to the package given as sin20=.342 cos20=.940
a 40 J
b. 42.2 J
c. 42.6 J
d. 45 J
Question 15.Consider the following two statements.
STATEMENT 1 Linear momentum of a system of particles is zero.
STATEMENT 2 Kinetic energy of system of particles is zero.
(A) A does not imply B and B does not imply A.
(B) A implies B but B does not imply A
(C) A does not imply B but b implies A’
(D) A implies B and B implies A.
Question 16.The Position vector of the center of mass of uniform semi circular ring of radius R and Mass M whose center coincided with the origin
a.r=(2R/π)j
b.r=(R/π)j
c.r=(4R/π)j
d. none of the these
Question 17.Chosse the correct option
a.if Workdone by the conservative force is positive then Potential energy decreases
b. Rate of change of momentum of many particles system is proportional to net external force on the system
c.The workdone by the conservative force in closed loop is zero
d. None of the above
Question 18.Two electrons(e) are the at the point (-a,0) and (a,0).Their mass is m.They are released from rest.The acceleration of the center of mass of the system when the electron at 4a distance apart
a. e2/64mπε0a2
b. zero
c. e2/16mπε0a2
d. none of the above
Question 19.The potential energy of a certain particle is given by
U=20x2+35z3.Find the vector force on it
a. -40xi-105z2k
b. 40xi-105z2k
c.-10xi-105z2k
d 40xi+105z2k
Matrix Match type
Question 20.
Column I
a. Frictional force
b. Gravitational force
c. Electrical force
d Viscous force
Column II
P. Workdone by the force in closed loop is zero
Q. Workdone by the force in closed loop is not zero
Question 21. A mass is whirled in a circular path with constant angular velocity and its angular momentum is L.If the string is now halve keeping the angular velocity same then angular momentum is
a. L
b. L/4
c. L/2
d. 2L
Question 22.A mass is moving with constant velocity along a line parallel to xaxis away from origin.its angular momentum with respect to origin is
a. is zero
b. remains constant
c. goes on increasing
d. goes on decreasing
Question 23.A cylinder rolls up the incline plane reaches some height and then roll down without slipping through out this section.The direction of the frictional force acting on the cylinder are
a. Up the incline while ascending and down the incline while descending
b.Up the incline while ascending and desending
c. down the incline while ascending and up the incline while descending
d.down the incline while ascending and desending
Question 24.A uniform sold sphere rolls on the horizontal surface at 20 m/s.it then rolls up the incline of 30.If friction losses are negligible what will be the value of h where sphere stops on the incline
a. 28.6 m
b 30 m
c. 28 m
d. none of these
Question 25. A cylinder of Mass M and radius R rolls down a incline plane of inclination θ.Find the linear accleration of the cylinder
a. (2/3)gsinθ
b.(2/3)gcosθ
c gsinθ
d none of these
Question 26 An ice skater spins with arms outstretch at 1.9 rev/s.Her moment of inertia at this time is 1.33 kgm2.She pulls her arms to increase her rate of spin.Her moment of inertia after she pulls her arm is .48kgm2.What is her new rate of spinning
a. 5.26 rev/s
b. 5.2 rev/s
c 4.7 rev/s
d. none of thes
Question 27. Moment of inertia of a uniform rod of lenght L and mass M about an axis passing through L/4 from one end and perpendicular to its lenght
a. 7ML2/36
b.7ML2/48
c. 11ML2/48
d.ML2/12
Question 28. A wheel starts from rest and spins with a constant angular acceleration. As time goes on the
acceleration vector for a point on the rim:
a. increases in magnitude but retains the same angle with the tangent to the rim
b.increases in magnitude and becomes more nearly radial
c. increases in magnitude and becomes more nearly tangent to the rim
d. decreases in magnitude and becomes more nearly radial
Question 29.
Two wheels are identical but wheel B is spinning with twice the angular speed of wheel A. The ratio of the
magnitude of the &radical acceleration of a point on the rim of B to the magnitude of the radial acceleration of
a point on the rim of A is:
a. 4
b . 2
c 1/2
d 1/4
Question 30. For a wheel spinning with constant angular acceleration on an axis through its center, the ratio of
the speed of a point on the rim to the speed of a point halfway between the center and the rim is:
a 2
b 1/2
c 4
d 1/4
Question 31. A wheel initially has an angular velocity of 18 rad/s. It has a constant angular acceleration of 2.0 rad/s2 and is
slowing at first. What time elapses before its angular velocity is18 rad/s in the direction opposite to its initial
angular velocity?
a 3 sec
b 6 sec
c 18 sec
d none of these
Question 32. One solid sphere X and another hollow sphere Y are of same mass and same outer radii. Their moment of inertia about their diameters are respectively Ix and Iy such that
(A) Ix= Iy
(B) Ix > Iy
(C) Ix < Iy
(D) Ix/Iy=Dx/Dy
Where Dx and Dy are their densities.
Question 33.Which of the following is noninertial frame of refrence
a. A train which speeding Up
b. A train with constant speed
c. A train which speeding down
d A train at rest
Question 34.what is of these is true for Projectile motion
a. Velcoity is perpendicular to acceleration at the highest point
b. Horizontal components of velocity remains constant through out the path
c. Range of the projectile is given by Horizontal component of velocity X Time of flight
d. None of the above
Question 35. A block of mass M is pulled along a horizontal friction surface by a rope of mass m. If a force P is applied at the free end of the rope, the force exerted by the rope on the block is
a)Pm/m+M
b)P
c)PM/m+M
d)Pm/M-m
Question 36.A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of 5 m/s2, the reading of the spring balance will be
(A) 24 N
(B) 74 N
(C) 15 N
(D) 49 N
Question 37. A particle moves in a straight line according to
x=t3-4t2+3t
Find the acceleration of the particle at displacement equal to zero
a.(-8,-2,10)
b. (-1,-2,10)
c. (8,2,10)
d. (1,2,10)
Detailed Solutions
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