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.
A spring of force constant k is cut into lengths of ratio 1:2:3. They are connected in series and the new force constant is . If they are connected in parallel and force constant is is
1. 1:6
2. 1:9
3. 1:11
4. 6:11
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