Four blocks A, B, C and D of equal mass are placed on the belt of conveyor at equal distances as shown. Mass of each block is 2 kg and distance between two blocks (d) is 400 mm. Assume masses of rollers (which cannot translate) and conveyor belt are negligible. Friction is sufficient to prevent the slipping between blocks and belt. Now, a constant force of 1000 N is applied on the belt, parallel to the belt as shown. Neglect the radius of roller as compared to d. The magnitude of velocity of block B when it leaves the roller at point T is 10√(7/α) m/s. Find the value of α.
Physics · Mixed Chapter
JEE Mains

Question

Four blocks A, B, C and D of equal mass are placed on the belt of conveyor at equal distances as shown. Mass of each block is 2 kg and distance between two blocks (d) is 400 mm. Assume masses of rollers (which cannot translate) and conveyor belt are negligible. Friction is sufficient to prevent the slipping between blocks and belt. Now, a constant force of 1000 N is applied on the belt, parallel to the belt as shown. Neglect the radius of roller as compared to d. The magnitude of velocity of block B when it leaves the roller at point T is 10√(7/α) m/s. Find the value of α.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The conveyor carries four 2 kg blocks initially, separated by d=0.4 m. It is pulled with force F=1000 N. Step 2: For the first d of belt travel, acceleration is F/(4×2)=125 m s⁻²; for the next d, after block A leaves, acceleration is F/(3×2)=1000/6 m s⁻². Step 3: Add changes in speed squared: v_B²=2(125)(0.4)+2(1000/6)(0.4)=100+400/3=700/3. Step 4: Thus v_B=10√(7/3) m s⁻¹; comparing with 10√(7/α) gives α=3.