DPP – 11 1. As shown in the figure, one end of rod which is fixed
to a support is connected by a thread which passes over a pulley and other end of thread is connected with the block of mass 10kg. A horizontal force of
3
50 N is applied on the rod. The system is in equilibrium. The value of is
(a) 300 (b) 600 (c) 900 (d) 00
m
50 3N
2. A rod AB is moving in a vertical plane. At a certain instant when the rod is inclined at 60° to the horizontal, the point A is moving horizontally at 3 m/s, while B is moving in the vertical
direction. The velocity of B is A vA
B vB 60° (a) 3 1 m/s (b) 2 3m/s (c) 3 m/s (d) 2 3 m/s
3. In the diagram shown, two blocks A and B having masses 4 kg & 2 kg are placed against a vertical wall as shown in figure. The co-efficient of friction between blocks and horizontal surface is 0.4. A horizontal force of 20 N is applied on block A. Then, the frictional force between block B and floor is (g = 10m/s2)
(a) 4 N (b) 5 N
(c) 16 N (d) 20 N
4. In the above problem, the contact force between block B and the wall is
(a) 20 N (b) 0 N
(c) 4 N (d) 10 N
5. A force F iˆ4jˆ acts on a block as shown. The force of friction acting on the block is
(a) iˆ (b) 1.8iˆ (c) 2.4iˆ (d) 3iˆ
6. A car begins to move at time t = 0 and then accelerates along a straight track with a velocity given by V(t) = 2t2 ms–1 for 0 < t < 2, where t is time in second. After the end of acceleration, the car continues to move at a constant speed. A small block initially at rest on the floor of the car begins to slip at t = 1 s and stops slipping at t = 3 s. The coefficient of static and kinetic friction between the block and the floor are s and k respectively. Find the value of k s 3 .
the slab at t = 0. Calculate the distance (in cm) moved by slab when the block has moved a distance of 0.5 m on the slab.
8. Two particles 1 and 2 are projected upwards from a point at the same instant with velocities of 5 m/sec and 10 m/sec respectively. Their angles of projection with vertical are 37° and 53° respectively and horizontal components of their velocities are in same direction. Find the time interval (in ms) between the moments when they pass through the other common point of their paths.
DPP – 12 1. A chain consisting of 5 links each of mass 0.1 kg is
lifted vertically with a constant acceleration of 2.5 m/s2 as shown in the figure. The force of interaction between the top link and the link just below it will be (a) 6.15 N (b) 4.92 N (c) 3.69 N (d) 2.046 N 1 2 3 4 5 F
2. Three blocks are connected as shown in the figure. The coefficient of friction at all surfaces is 0.25. The acceleration of B when external force is 4 mg will be (a) 20 g (b) 10 g (c) 20 3g (d) zero
3. A block of mass 2 kg is given a push horizontally and then the block starts sliding over a horizontal plane. The graph shows the velocity-time graph of the motion. The co-efficient of friction between the plane and the block is
(a) 0.02 (b) 0.2 (c) 0.04 (d) 0.4
4. A system of masses is shown in the figure with masses & co-efficients of friction indicated. The maximum value of F for which there is no slipping anywhere is
(a) 56.25 N (b) 90 N (c) 112.5 N (d) 150 N
5. In the above problem, the minimum value of F for which B slides on C is (a) 56.25 N (b) 90 N (c) 112.5 N (d) 150 N
6. Figure shows a hemisphere and a supported rod. Hemisphere is moving right with a uniform velocity v2 and the end of rod which is in contact with ground is moving left with a velocity v1. Find the rate (in rad/s) at which the angle is decreasing at the moment when = 45°. (Take R = 2 m, v1 v2 4m/s)
R
v1 v2
7. A man of mass 50 kg is standing on one end of a stationary wooden plank resting on a frictionless surface. The mass of the plank is 10 kg, its length is 300 m and the coefficient of friction between the man and the plank is 0.2. Find the shortest time (in s) in which the man can reach the other end of the plank starting from rest and stopping at the other end.
horizontal channel. The sides of the channels are smooth, but at the interfaces of A and B, which are at 45° with the horizontal, there exists a static coefficient of friction = 0.4. What is the minimum force F (in N) that must be applied horizontally to A to start motion of the latch B if it has a mass
DPP – 13
1. Three identical rigid circular cylinders A, B and C are arranged on smooth inclined surfaces as shown in figure. The least value of that prevents the arrangement from collapse is (a) 2 1 tan 1 (b) 3 1 tan 1 (c) 3 3 1 tan 1 (d) 3 4 1 tan 1 2. A 2m wide truck is moving with a uniform speed v0 = 8 m/s
along a straight horizontal road. A pedestrian starts to cross the road with a uniform speed v when the truck is 4 m away from him. The minimum value of v so that he can cross the road safely is v0 v man 4m Truck 2m (a) 2.62 m/s (b) 4.6 m/s (c) 3.57 m/s (d) 1.414 m/s
3. A particle is projected with a speed of 100 m/s at angle = 60° with the horizontal at time t = 0. At time t the velocity vector of the particle becomes perpendicular to the direction of velocity of projection. Its tangential acceleration at time t is
(a) 10 m/s2 (b) 5 3m/s2 (c) 5 m/s2 (d) zero
4. In the above problem, its radius of curvature at time t is
(a) 3 km (b)
3 3
2
km (c) 2 km (d) 2 km
5. To a block of mass 1 kg a horizontal force of 3
10
N is applied horizontally as shown in the figure. The frictional force acting on the block is (a) zero (b) N 3 10 (c) 3 20 N (d) 5 N
6. A student is standing on a train travelling along a straight horizontal track at a speed of 10 m/s. The student throws a ball into the air along a path, that makes an initial angle of 60° with the horizontal along the track as observed by the student. The professor standing on the ground observes the ball to rise vertically. What will be the maximum height (in m) reached by the ball.
7. A particle of mass 2.5 kg is moving in gravity free space with velocity of 3 m/s. At t = 0, a iˆ
force of magnitude 67.5 N starts acting on the particle such that it is always perpendicular to its instantaneous velocity. Find the minimum time (in ms) after which the particle has the same velocity as the initial. ( = 3.14)
circumference. Find ratio of 2 2 2 and dt d dt d at the moment when = 45°.
DPP – 14
1. A cat wants to catch a rat. The cat follows the path whose equation is x y0. But rat follows the path whose equation is 2 y2 4
x . The co-ordinates of possible points of catching the rat are
(a) ( 2, 2) (b) ( 2, 2)
(c) ( 2, 3) (d) (0, 0)
2. In the arrangement shown, end A of light inextensible string is pulled up with constant velocity v. The velocity of block
B is (a) v/2 (b) v (c) v/3 (d) 3v A v B
3. A particle is projected with a velocity u, at an angle , with the horizontal. Time at which its vertical component of velocity becomes half of its net speed at the highest point will be (a) g u 2 (b) 2g
sin cos
u (c)
2cos sin
2g u (d)
2sin cos
2g u4. Tangential acceleration of a particle moving in a circle of radius 1 m varies with time t (initial velocity of particle is zero) as shown in figure. Time after which total acceleration of particle makes an angle of 30° with radial acceleration is
(a) 4 sec (b) 3 4 sec (c) 3 2 2 sec (d) 2 sec
5. A man is standing on a rough (= 0.5) horizontal disc rotating with constant angular velocity of 5 rad/sec. Distance from centre at which he should stand so that he does not slip on the disc is
(a) R0.2m (b) R0.2m (c) R0.5m (d) R0.3m
6. Particle A is moving in a horizontal plane with constant velocity V as shown. Another particle B is moving in a circle of radius 1 m with same speed V. At the moment when A is diametrically opposite to B, find the radius of curvature (in m) of B as seen by A at this moment.
under the action of a force F = 2 r Km
directed (r = position of bead from P &
K = constant) towards a point P with in the circle at a distance 2
R
from the centre. What should be the minimum velocity (in m/s) of bead at the point of the wire nearest the centre of force (P) so that bead will complete the circle (Take 8unit)
3R k
8. A ball is attached to an end of a light inextensible string, the other end of which is fixed at the origin. The ball moves in vertical x-y plane where x is along horizontal and y along vertical. At the top of its trajectory, when string is straight it’s velocity is 5 m/s. What iˆ
will be the angular velocity (in rad/s) when ball is at the bottom of the trajectory. [length of string = 0.5 m]
