T hree block s of m ass es m 1, m 2 and M are arranged as s hown in f igu re.

All the surf ac es are frictionles s

1 and str ing is inex ten s ible. Pulleys are light. A c onstant f orc e F is applie d on block of m as s m . Pulleys
1
and string are light. Part of the string connecting both pulleys is vertical and part of the strings connecting
pulleys with masses m and m are horizontal.

F
(A) Acceleration of mass m 1 (P) m
1

F
(B) Acceleration of mass m 2 (Q) m  m
1 2
(C) Acceleration of mass M (R) zero
m 2F
(D) Tension in the string (S) m  m
1 2
Sol. (A) Q (b) Q (C) R (D) S

2. For the following system shown assume that pulley is frictionless, string is massless (m remains on M) :

Find
(a) the acceleration of the block A.
(b) Normal reaction on m is (force on C due to B)
(c) the force on the ceiling

mg 2Mmg (6M  5m) Mg

Ans. (a) 2M  m (b) 2M  m (c) 2M  m

3. A small block B is placed on another block A of mass 5 kg and length 20 cm. Intially the block B is near the
right end of block A (figure). A constant horizontal force of 10 N is applied to the block A. All the surfaces
are assumed frictionless. Find the time elapsed before the block B separates from A

Ans. 0.45 s
Passage (4 to 8)
Figure shows a weighing machine kept in a lift. Lift is moving upwards with acceleration of 5 m/s 2. A
block is kept on the weighing machine. Upper surface of block is attached with a spring balance. Reading
shown by weighing machine and spring balance is 15 kg and 45 kg respectively.
Answer the following questions. Asume that the weighing machine can measure weight by having negligible
deformation due to block, while the spring balance requires larger expansion :(take g = 10 m/s2)

4. Mass of the object in kg is : Ans :40 kg

5. In the above situation normal acting on the block as seen by an observer in the lift.

Ans :15 kg
M
Weighing
6. If lift is stopped and equilibrium is reached. Reading of weighing machine will be : Machine

(Ans) zero

7. If lift is stopped and equilibrium is reached. Reading of spring balance will be :

(A) zero (B) 20 kg (C) 10 kg (D*) 40 kg

8. Find the acceleration of the lift such that the weighing machine shows its true weight(spring
balance reaction remains same).

45 85 22 60
(A*) m/s 2 (B) m/s2 (C) m/s2 (D) m/s2
4 4 4 4

Passage (9 to 11 )

Two smooth blocks are placed at a smooth corner as shown. Both the blocks are having mass m. We apply
a force F on the small block m. Block A presses the block B in the normal direction, due to which pressing 
force on vertical wall will increase, and pressing force on the horizontal wall decrease, as we increase F. ( =
37° with horizontal). As soon as the pressing force on the horizontal wall by block B becomes zero, it will
loose the contact with the ground. If the value of F is further increased, the block B will accelerate in upward
direction and simultaneously the block A will move toward right.

9. What is minimum value of F, to lift block B from ground :

25 5 3 4
(A) mg (B) mg (C*) mg (D) mg
12 4 4 3

10. If both the blocks are stationary, the force exerted by ground on block A is :

3F 3F 4F 4F
(A) mg + (B) mg – (C*) mg + (D) mg –
4 4 3 3
 11. If acceleration of block A is a rightward, then acceleration of block B will be :

3a 4a 3a 4a
(A*) upwards (B) upwards (C) upwards (D) upwards
4 3 5 5

12. In the arrangement shown in Fig. the mass of the rod M exceeds the mass m of the ball. The ball has an

opening permitting
Irodov_1.74

it to slide along the thread with some friction. The mass of the pulley and the friction in its axle are
negligible. At the initial moment the ball was located opposite the lower end of the rod. When set free,
both bodies began moving with constant accelerations. Find the friction force between the ball and the
thread if t seconds after the beginning of motion the ball got opposite the upper end of the rod. The rod
length equals .
[Ans : Ffr = 2 mM / (M – m)t2 ]

13. A block B of mass 0.6 kg slides down the smooth face PR of a wedge A of mass 1.7 kg which can move
freely on a smooth horizontal surface. The inclination of the face PR to the horizontal is 45º. Then :

(A*) the acceleration of A is 3 g/20

(B*) the vertical component of the acceleration of B is 23 g/40
(C*) the horizontal component of the acceleration of B is 17 g/40
(D) none of these

14. Neglecting friction every where, find the acceleration of M. Assume m > m .

(m  m')g
2M  3m  3m'
[ Ans: a = ]