A simple pendulum hangs from the roof of a train moving on horizontal rails. If the string is inclined towards the front of the train, then train is-
1. Moving with constant velocity
2. In accelerated motion
3. In retarded motion
4. At rest
The value of \(M\) of the hanging block is in the figure, which will prevent the smaller block (\(m\)\(=\)\(1\) kg) from slipping over the triangular block. All the surfaces are smooth and string and pulley are ideal. (Given: \(M'\)\(=4\) kg and \(\theta\) \(=37^\circ\))
1. \(12\) kg
2. \(15\) kg
3. \(10\) kg
4. \(4\) kg
While walking on ice one should take small steps to avoid slipping. This is because smaller steps ensure
1. Larger friction
2. Smaller friction
3. Larger normal force
4. Smaller normal force
A block is placed on a rough horizontal plane. A time dependent horizontal force F=kt acts on the block. The acceleration time graph of the block is :
1.
2.
3.
4.
A rod of length L and mass m is acted on by two unequal forces and as shown in the following figure
The tension in the rod at a distance y from the end A is given by :
1.
2.
3.
4. None of the above
Two blocks A and B of masses m & 2m respectively are held at rest such that the spring is in natural length. Find the accelerations of both the blocks just after release.
(1)
(2)
(3) (0, 0)
(4)
Two blocks 'A' and 'B' each of mass 'm' are placed on a smooth horizontal surface. Two horizontal force F and 2F are applied on both the blocks 'A' and 'B' respectively as shown in figure. The block A does not slide on block B. Then the normal reaction acting between the two blocks is:
(1) F
(2) F/2
(3)
(4) 3F
Two masses, m and M, are connected by a light string passing over a smooth pulley. When mass m moves up by 1.4 m in 2 sec, the ratio is:
1. | \(\frac{13}{15} \) | 2. | \(\frac{15}{13} \) |
3. | \(\frac{9}{7} \) | 4. | \(\frac{7}{9}\) |
Two masses M and m are attached to a vertical axis by weightless threads of combined length l. They are set in rotational motion in a horizontal plane about this axis with constant angular velocity ω. If the tensions in the threads are the same during motion, the distance 'x' of M from the axis is-
(1)
(2)
(3)
(4)
A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved
(1) 14 m/s
(2) 3 m/s
(3) 3.92 m/s
(4) 5 m/s
A point mass m is suspended from a light thread of length l, fixed at O, and is whirled in a horizontal circle at a constant speed as shown. From your point of view, stationary with respect to the mass, the forces on the mass are:
1. | 2. | ||
3. | 4. |
A motor cycle driver doubles its velocity when he is having a turn. The force exerted outwardly will be
(1) Double
(2) Half
(3) 4 times
(4) times
A mass is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity ω0. If the length of the string and angular velocity are doubled, the tension in the string which was initially T0 is now
(1) T0
(2) T0/2
(3) 4 T0
(4) 8 T0
A bucket tied at the end of a 1.6 m long string is whirled in a vertical circle with constant speed. What should be the minimum speed so that the water from the bucket does not spill, when the bucket is at the highest position (Take g = 10 m/s2)
(1) 4 m/sec
(2) 6.25 m/sec
(3) 16 m/sec
(4) None of the above
An object with a mass 10 kg moves at a constant velocity of 10 m/sec. A constant force then acts for 4 second on the object and gives it a speed of 2 m/sec in opposite direction. The acceleration produced in it, is
(1) 3 m/sec2
(2) –3 m/sec2
(3) 0.3 m/sec2
(4) –0.3 m/sec2
A machine gun is mounted on a 2000 kg car on a horizontal frictionless surface. At some instant the gun fires bullets of mass 10 gm with a velocity of 500 m/sec with respect to the car. The number of bullets fired per second is ten. The average thrust on the system is
(1) 550 N
(2) 50 N
(3) 250 N
(4) 250 dyne
A cricket ball of mass 250 g collides with a bat with velocity 10 m/s and returns with the same velocity within 0.01 second. The force acted on bat is
(1) 25 N
(2) 50 N
(3) 250 N
(4) 500 N
A plumb line is suspended from a ceiling of a car moving with horizontal acceleration of a. What will be the angle of inclination with vertical
1. tan–1(a/g)
2. tan–1(g/a)
3. cos–1(a/g)
4. cos–1(g/a)
A block of mass m is placed on a smooth wedge of inclination θ. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block (g is acceleration due to gravity) will be
(1)
(2)
(3) mg
(4)
The linear momentum p of a body moving in one dimension varies with time according to the equation p = a + bt2 where a and b are positive constants. The net force acting on the body is
(1) A constant
(2) Proportional to t2
(3) Inversely proportional to t
(4) Proportional to t
A man is standing at a spring platform. Reading of spring balance is 60 kg-wt. If a man jumps outside the platform, then reading of spring balance:
(1) first increases then decrease to zero.
(2) decreases.
(3) increases.
(4) remains same.
A block of mass 4 kg is suspended through two light spring balances A and B. Then A and B will read respectively
(1) 4 kg and zero kg
(2) Zero kg and 4 kg
(3) 4 kg and 4 kg
(4) 2 kg and 2 kg
The mass of a body measured by a physical balance in a lift at rest is found to be m. If the lift is going up with an acceleration a, its mass will be measured as:
(1)
(2)
(3) m
(4) Zero
In the arrangement shown in the figure, the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed
1.
2.
3.
4.
On the horizontal surface of a truck (μ = 0.6), a block of mass 1 kg is placed. If the truck is accelerating at the rate of 5m/sec2 then frictional force on the block will be
(1) 5 N
(2) 6 N
(3) 5.88 N
(4) 8 N
A force-time graph for a linear motion is shown in figure where the segments are circular. The linear momentum gained between zero and 8 second is
1.
2.
3.
4.
Two blocks A and B of masses 3m and m respectively are connected by a massless and inextenisible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively
1.
2.
3.
4.
One end of the string of length l is connected to a particle of mass m and the other end is connected 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) will be: (T represents the tension in the string)
1. | \(T \) | 2. | \(T+\frac{m v^2}{l} \) |
3. | \(\mathrm{T}-\frac{m v^2}{l} \) | 4. | \(\text{Zero}\) |
A car is negotiating a curved road of radius R. The road is banked at angle . The coefficient of friction between the tyres of the car and the road is . The maximum safe velocity on this road is
1.
2.
3.
4.
Three blocks A, B and C of masses 4 kg, 2 kg and 1 kg respectively, are in contact on a frictionless surface, as shown. If a force of 14 N is applied on the 4 kg block, then the contact force between A and B is
1.2N
2. 6N
3. 8N
4. 18N
A block A of mass m1 rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of table and from its other end another block B of mass m2 is suspended. The coefficient of kinetic friction between the block and the table is μk. When the block A is sliding on the table, the tension in the string is
1. (m2+μkm1)g /(m1+m2)
2. (m2-μkm1)g/(m1+m2)
3. m1m2(1+μk)g/(m1+m2)
4. m1m2(1-μk)g/(m1+m2)
A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30°, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be. respectively
1. 0.6 and 0.6
2. 0.6 and 0.5
3. 0.5 and 0.6
4. 0.4 and 0.3
Two stones of masses m and 2m are whirled in horizontal circles, the heavier one in a radius r/2 and the lighter one in radius r. The tangential speed of lighter stone is n times that of the value of heavier stone when they experience same centripetal forces. The value of n is
1. 2
2. 3
3. 4
4. 1
A system consists of three masses m1, m2 and m3 connected by a string passing over a pulley P. The mass hangs freely and m2 and m3 are on a rough horizontal table (the coefficient of friction=μ) The pulley is frictionless and of negligible mass. The downward acceleration of mass m1, is (Assume,m1=m2=m3=m)
1. g(1-gμ)/9
2. 2gμ/3
3. g(1-2μ)/3
4. g(1-2μ)/2
A balloon with mass m is descending down with an acceleration a (where a < g). How much mass should be removed from it so that it starts moving up with an acceleration a?
1. 2ma/g+a
2. 2ma/g-a
3. ma/g+a
4. ma/g-a
Three blocks with masses m, 2m and 3m are connected by strings, as shown in the figure. After an upward force, F is applied on block m, the masses move upward at constant speed v. What is the net force on the block of mass 2m? (g is the acceleration due to gravity)
1. Zero
2. 2mg
3. 3mg
4. 6mg
The upper half of an inclined plane of inclination θ is perfectly smooth while the lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom if the coefficient of friction between the block and lower half of the plane is given by
1. μ=1/tanθ
2. μ=2/tanθ
3. μ=2tanθ
4. μ=tanθ
A car of mass 1000 kg negotiates a banked curve of radius 90m on a frictionless road. If the banking angle is ,the speed of the car is
1. 20 2. 30
3. 5 4. 10
A person of mass 60 kg is inside a lift of mass 940 kg and presses the button on control panel. The lift starts moving upwards with an acceleration . If , the tension in the supporting cable is:
1. 9680 N
2. 11000 N
3. 1200 N
4. 8600 N
A conveyor belt is moving at a constant speed of 2 m/s. A box is gently dropped on it. The coefficient of friction between them is The distance that the box will move relative to the belt before coming to rest on it taking , is
1. 2.
3. zero 4.
A block of mass m is in contact with the cart C as shown in the figure.
The coefficient of static friction between the block and the cart is The acceleration of the cart that will prevent the block from falling satisfies
1. 2.
3. 4.
A gramophone record is revolving with an angular velocity A coin is placed at a distance r from the centre of the record. The static coefficient of friction is The coin will revolve with the record if:
1. 2.
3. 4.
A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is 20m. The speed of the car at the top of the hill is between:
1. 14m/s and 15m/s
2. 15m/s and 16m/s
3. 16m/s and 17m/s
4. 13m/s and 14m/s
A particle of mass m is projected with velocity v making an angle of with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be
1. 2mv
2. mv/
3. mv
4. zero
Sand is being dropped on a conveyor belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity of v m/s will be
1. Mv newton
2. 2Mv newton
3. newton
4. zero