Mechanics Revision Paper

8/14/2019 Mechanics Revision Paper

1/18

Mohammed

Asif

Name :

Roll No. :

Topic : MechanicsRevision Paper

Ph : 9391326657, 64606657

Mechanics-Revision Paper1. A particle moving along a straight line with uniform acceleration has velocities 7m/s at P and

17m/s at Q. R is the mid-point of PQ. Then

a) The average velocity between R and Q is 15 m/s

b) The average velocity between P and R is 15 m/s

c) The average velocity between P and Q is 25 m/s

d) The average velocity between P and R is 24 m/s

2. The path of a projectile as seen form another projectile, given u1, u2 and 21, are velocities

and angle of projection:

a)

=1122

1122

coscos

sinsin

uu

uu

x

yb)

=1122

1122

2coscos

sinsin

uu

uu

x

y

c)

2

22

2

2

1

22

1

1

cos2tan

cos2tan

u

g

u

g

x

y

= d) It will be hyperbola

3. A ball is dropped form a certain height on a horizontal floor. The coefficient of restitutionbetween the ball and floor is . The speed-time graph in this situation will be:

a) b) c) d)

4. A small particle of mass m is released form rest from point A inside a smooth hemispherical

bowl as shown in figure. The ratio of (x) of magnitude of centripetal force and normal reaction

on the particle at any point B varies with as:

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a) b) c) d)

5. The potential energy of a particle of mass 5kg moving in the x-y plane is given by U = -7x+24y

joule. x and y being in m. Initially at t = 0, the particle is at the origin, moving with a velocity of

+

^^

7.04.26 ji m/s. The magnitude of force on the particle is:

a) 25 units b) 24 units c) 7 units d) None of these

6. Consider, the non-uniform circular motion in a vertical plane, as shown in figure. If vL is the

velocity at lower point, then for oscillation, leaving the circle, for looping the range of v L will be

respectively.

a) grvgrvgrv LLL 5,80,20 >

b) grvgrvgrgrv LLL 5,52,20


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a) b) c) d)

10. A ball of mass m flying horizontally with speed u hits a wedge of the same mass resting on arough horizontal surface. If 1 be the coefficient of friction between the ball and the wedge

and 2 be the same between the wedge and the horizontal surface and the duration of impact

between tea ball and the wedge be very small, then, for the duration of impact linear

momentum of the system ball + wedge can be assumed to be conserved

a) Along the horizontal direction only

b) Along the vertical direction obly

c) Along both the horizontal and vertical directions

d) Neither along the horizontal nor along the vertical directions.

11. As the work done by constant force in a closed path is always zero, a constant force is always

conservative in nature. Suppose a constant force along x is given by Fx = -6N. Find the potentialenergy function associated with this force if U = 0 at x = 5.

a) -6x 30 b) 6x 30 c) 6x + 30 d) -6x + 30

12. A ball falls to the ground from height h and bounces to height h. Momentum is conserved in

the ball-earth system:

a) No matter what height h it reaches b) Only if h < h

c) Only if h = h d) Only if h > h.

13. A particle of mass 50 which is at rest explodes into 3 fragments. Two equal fragments each of

mass 2m are found to move with a speed v each in opposite directions. What is the energy

released in the process of explosion. Neglect the energy loss in the form of sound and light.a)

2vm b) 2

2vm c) 3

2vm d) 4

2vm

14. A rocket of initial mass 5000kg ejects gas at a constant rate of 6kg/s with a relative speed of

2050m/s. Acceleration of the rocket 15 second after it is blasted off from the surface of earth

will be (g = 10m/s2).

a) 10 m/s2 b) 20 m/s2 c) 30 m/s2 d) 40 m/s2

15. A block of mass M is tied to one end of a mass less rope. The other end of the rope is in the

hands of a man of 2M as shown in the figure. The block and the man are resting on a rough

wedge of mass M as shown in the figure. The whole system is resting on a smooth horizontal

surface. The man pulls the rope. Pulley is mass less and frictionless. What is the displacement ofthe wedge when the block meets the pulley. (Man does not leave his position during the pull)




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a) 0.5 m b) 1 m c) zero d) m32

16. The displacement time graph for a particle moving along a straight line is given below:

Choose the correct statement for the motion described by above graph:

a) The acceleration at F is zerob) The acceleration at D may be zero

c) The accelerations at D must be zero

d) The total distance travelled will be more than the magnitude of the total displacement.

17. A particle is projected form the ground. If the equation of the trajectory is2

2xxy = , then

time of flight is

a) g/2 b) g/3 c) g/9 d) g/2

18. In the arrangement shown in the figure the block A is moving on a stationary horizontal surface

connecting the block A with the pulley Q and the block B with a support. S, moving in thevertically upward direction are inextensible. At certain moment if the block A is moving

towards right at s speed of 4m/s and the supports S is moving upwards at a speed of 5m/s, then

the block B is moving in the downward direction at a speed of

a) 13 m/s b) 9 m/s c) 7 m/s d) 0 m/s

19. Find minimum height of obstacle so that the sphere can stay in equilibrium.




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a) cos1+

R

b) sin1+

R

c)( )sin1R

d) a) cos1+

R

20. Two light vertical springs with equal natural lengths and spring constants k1 and k2 are

separated by a distance l. Their upper ends are fixed to the ceiling and their lower ends to the

ends A and B of a light horizontal rod AB. A vertical downwards force F is applied at point C

the rod. AB will remain horizontal in equilibrium if the distance AC

a)2

lb)

12kk

l

+ c)12

1

kk

kl

d)12

2

kk

kl

+

21. A particle is moving in a circular orbit of radius r1 with an angular velocity 1 . It jumps to

anther circular orbit of radius r2 and attains an angular velocity 2. If 12 5.0 rr = and

assuming that no external torque is applied to the angular velocity 2, is given by:

a) 12 4 = b) 12 3 = c) 12 2 = d) 12 =

22. In the figure shown a rin A is initially rolling without sliding with a velocity v on the horizontalsurface of the body B (of same mass as A). All surfaces are smooth. B has no initial velocity.

What will be maximum height reached by A on B.

a)g

v

4

32

b)g

v

4

2

c)g

v

2

2

d)g

v

3

2

23. The dumbbell is placed on a frictionless horizontal table. Sphere A is attached to a frictionless

pivot so that B can be made to rotate about A with constant angular velocity. If B makes onerevolution in period P, the tension in the rod is




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a)2

24

P

Mdb)

2

28

P

Mdc)

P

Md2

4d)

P

Md2

24. A uniform rod of length L rests against a smooth roller as shown in figure. Find the friction

coefficient between the ground and the lower end if the minimum angle the rod can make with

the horizontal is .

a)

sincos2

sincos

2

2

Lh

L

+b)

sincos2

sincos

2

2

Lh

L

c)

cossin2

coscos

2

2

Lh

L

+d) None of these

25. Find the height h to which a man of mass m can jump ifPis the maximum power, the man can

use and is the height of centre of mass of man from ground.

a)2

1

4

2

1

=

m

ps

gh b)

2

1

4

4

1

=

m

ps

gh c)

3

2

4

2

1

=

m

ps

gh d) None of these

26. In a vertical circle, AB is the horizontal diameter. Let AD and AE are two chords of the circle

which subtend the angle and 2 at the centre of the circle respectively. If a particle slides

along the two chords from A to D and A to E and the ratio of the time duration it take to travel

the distances AD and AE is 1:n then which of the following is correct

a) ( ) 1cos12 = n b) ( ) 1cos12 =+ n c) ( ) 0cos12 = n d) None of these

27. A heavy particle of mass m is in motion on a smooth surface of a hemisphere of radius R and

three is no friction. At the initial instant the particle is at the topmost point A and has an initial

velocity v0.. At what point will the particle leave the surface of the hemisphere? Particle will

leave the sphere at the initial instant.

a)

+=

Rg

v

33

2cos

2

01 b)

=

Rg

v

33

2cos

2

01 c)

=

Rg

v

33

2sin

2

01 d) 0=

28. A 2kg block rests over a small hole in a table. A woman beneath the table shoots a 15gm bullet

through the hole into the block, where it iodges. How fast was the bullet going if the block rises75cm above the table?

a) 525 m/s b) 515 m/s c) 625 ms/ d) 615 m/s




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29. A chain of mass m and length 1 rests on a rough surfaced table so that one of its ends hangsover

the edge. The chain start sliding off the table all by itself provided the overhanging part equals

1/3 of the chain length. What will be the total work performed by the friction forces acting on

the chain by the moment it slides completely off the table? Friction coefficient is .

a)9

2 lgM b)

9

2 lgMc)

3

2 lgM d)

3

2 lgM

30. A man weighing 80kg is standing in a trolley weighing 320kg. The trolley is resting on

frictionless horizontal rails. If the man starts walking on the trolley with a speed of 1m/s, then

after 4s his displacement relative to the ground will be

a) 5 m b) 4.8 m c) 3.2 m d) 3.0 m




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KEY1) a 2) a 3) b 4) a 5) a

6) 7) a 8) d 9) a 10) d

11) b 12) a 13) b 14) a 15) a

16) d 17) a 18) a 19) d 20) d

21) a 22) b 23) b 24) b 25) c

26) a 27) a 28) b 29) 30) c

Solutions1. Let a be the acceleration and lbe the distance between P and Q, then using asuv 222 += , we

get.

Therefore, velocity at R is

2..2

2 laVV PR +=

laVP +=2

2

7177

22

2 +=

132

17722

=+

=

Therefore, average velocity between P and R is

21

RP VVV+

=>< [a is constant]

sm /102

137=

+=

Therefore, average velocity between R and Q is

smVV

VQR

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1713

21

=+

=+

=>

Mechanics Revision Paper

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