1 1 A trolley T of mass 5kg on a horizontal smooth surface

Two long current carrying thin wires both with current I are held by insulating threads of length L and are in equilibrium as shown in the figure with threads making an angle 0 with the vertical If wires have mass per unit length then the value of I is g gravitational acceleration a 2 ngL PO c sin 0 Owl tan 0 n gL Vui Po cos 0 Tom b L n gL V Mo d 2 sin 0 tan 0 n gL Ho cos 0 11

with angle of inclination 8 Various values of 0 are given in Column I The coefficient of friction between the 1 kg another mass m 2 kg are placed together see figure on an inclined plane block m and the plane is always zero The coefficient of static and dynamic friction between the block m and the plane are equal to 0 3 In Column Il expressions for the friction on block m are given Match the correct expression of the friction in Column II with the angles given in Column I and choose the correct option The acceleration due to gravity is denoted by g Useful information tan 5 5 0 1 tan 11 5 0 2 tan 16 5 0 3 A 5 B 0 10 C 8 15 D 8 20 Code A 1 P Mi Column I B P C p D r m m Column II p m g sine q m m g sine r m g cose s m m g cose

20 N 1 0 kg Figure 5 ES 5 Consider the situation shown in figure 5 E9 All the surfaces are frictionless and the string and the pulley are light Find the magnitude of the acceleration of the two blocks 0 98 N 1 F 3m 5m Figure 5 E9 m 4 m A constant force F m g 2 is applied on the block of mass m as shown in figure 5 E10 The string and the pulley are light and the surface of the table is smooth Find the acceleration of m Figure 5 E10 M F 1 0 kg 32 N Figure 5 E11 m 27 In figure 5 E11 m 5 kg m 2 kg and F 1 N Find the acceleration of either block Describe the motion of m if the string breaks but F continues to act Mag mitm 4 3 28 Let m 1 kg m 2 kg and m 3 kg in figure 5 E12 Find the accelerations of m m and m The string from the upper pulley to m is 20 cm when the system is released from rest How long will it take before m strikes the pulley 20cm m 29 In the previous problem suppose m 20 kg and m 30 kg What should be the mass m so that it remains at rest 2 M Figure 5 E12 30 Calculate the tension in the string shown in figure 5 E13 The pulley and the string are light and all surfaces are frictionless Take g 10 m s M 1 kg Figure 5 E13 31 Consider the situation shown in figure 5 E14 Both the pulleys and the string are light and all the surfaces are frictionless a Find the acceleration of the mass M b Find the tension in the string c Calculate the force exerted by the clamp on the pulley A in the figure B O Figure 5 E14 30 1 kg Figure 5 E15 MO 32 Find the acceleration of the block of mass M in the situation shown in figure 5 E15 All the surfaces are frictionless and the pulleys and the string are light 9 3 5N 2 M 29 13 Mg 13 2 Mg 3

8 A body is dropped from a certain height h h is very large and second body is thrown downward with velocity of 5 m s simultaneously What will be difference in heights of the two bodies after 3 s 2 10 m 4 20 m 3 15 m

Two blocks A and B of same mass m attached with a light spring are suspended by a string as shown in figure Find the acceleration of block A and Bjust after the string is cut A g 0 C g g B B 2g g g 2 D g mg kx Fos B A C

A particle moving with uniform retardation covers distances 18m 14m and 10m in successive seconds It comes to rest after travelling a further distance of 1 50 m 2x8m 3 12m 4 42m

discs of mass in and 4m having radii of a and 2a respectively are rigidly fixed by a massless rigid rod of length 1 24a through their centres This assembly is laid on a firm and flat surface and set rolling without slipping on the surface so that the angular speed about the axis of the rod is wo The angular momentum of the entire assembly about the point O is I see the figure Which of the following statement s is are true JEE Adv 2016 4m O a b m 2a 0 The centre of mass of the assembly rotates about the z axis with an angular speed of co 5 The magnitude of angular momentum of center of mass of the assembly about the point O is 81 ma co c The magnitude of angular momentum of the assembly about its center of mass is 17 ma 2

by a 10 Figure 6 W15 shows triang string placed on the two inclined parts of a structure The coefficients of static and kinetic fri are 0 28 and 0 25 respectively at each of the surface Find the minimum and maximum values of m for the system remains at rest b Find the acceleratio either block if m is given the minimum value calcul in the first part and is gently pushed up the inclin a short while m 45 45 Figure 6 W15 2 kg

23 arrangement shown below A m UL b g g 2m B Accelerations of masses A and B just after cutting the string Care a 0 g Dolc c sa d 2g g

15 The block of mass m shown in figure 12 E2 is fastened to the spring and the block of mass m is placed against it a Find the compression of the spring in the equilibrium position b The blocks are pushed a further distance 2 k m m g sine against the spring and released Find the position where the two blocks separate c What is the common speed of blocks at the time of separation from k mmmm my m 0 Figure 12 E2 19 kn m m 9 kn m gsin