Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.
Start Practicing

Worksheet: Motion of Two Bodies One of Which Is on a Horizontal Table and the Other Moves Vertically Downward

Q1:

Two bodies of masses 590 g and π‘š g are attached to the ends of a light inextensible string passing over a smooth pulley fixed to the edge of a smooth horizontal table. The first body rests on the table, and the other hangs freely vertically below the pulley. If the tension in the string is 90 860 dynes, determine the acceleration of the system. Take 𝑔 = 9 . 8 / m s 2 .

Q2:

A mass π‘š 1 rests on a smooth horizontal table. It is connected by a light inextensible string passing over a smooth pulley fixed at the edge of the table to another mass π‘š 2 hanging freely vertically below the pulley. A mass of 6.69 kg was added to π‘š 1 . When this system was released from rest, it accelerated at 7 2 0 𝑔 . Another mass of 6.75 kg was added to π‘š 1 . As a result, the acceleration of the system slowed to 1 3 5 0 𝑔 . Determine π‘š 1 and π‘š 2 . Take 𝑔 = 9 . 8 / m s 2 .

  • A π‘š = 1 1 . 5 2 9 1 k g , π‘š = 1 4 . 7 2 1 2 k g
  • B π‘š = 1 9 . 5 7 4 1 k g , π‘š = 1 4 . 1 4 2 2 k g
  • C π‘š = 1 9 . 4 2 5 1 k g , π‘š = 1 4 . 0 6 2 2 k g
  • D π‘š = 5 . 9 8 5 1 k g , π‘š = 6 . 8 2 5 2 k g

Q3:

A body of mass π‘š 1 rests on a smooth horizontal table at a distance of 11.76 m from its edge. It is connected by a light inextensible string passing over a smooth pulley fixed at the edge of the table to another body of mass π‘š 2 hanging freely vertically below the pulley. Given that, when the system was released from rest, the mass π‘š 1 took 3 seconds to reach the edge of the table, find the ratio π‘š ∢ π‘š 1 2 . Take the acceleration due to gravity 𝑔 = 9 . 8 / m s 2 .

  • A 4 ∢ 1 9
  • B 5 ∢ 4
  • C 4 ∢ 1 5
  • D 1 1 ∢ 4

Q4:

A body of mass 809 g rests on a smooth horizontal table. It is connected by a light inextensible string passing over a smooth pulley fixed at the edge of the table to another body of mass π‘š g hanging freely vertically below the pulley. Given that the tension in the string is 138 339 dynes, find the value of π‘š .Take 𝑔 = 9 . 8 / m s 2 .

Q5:

Two bodies of mass of 15 and 16.5 kilograms respectively were attached to the ends of a light inextensible string which passed over a smooth pulley fixed to the edge of a horizontal table. The body of larger mass was placed on the table while the smaller one was hanging vertically below the pulley. Determine the tension in the string, given that the acceleration due to gravity 𝑔 = 9 . 8 / m s 2 .

Q6:

A body rests on a smooth horizontal table. It is connected, by a light inextensible string passing over a smooth pulley fixed at the edge of the table, to another body hanging freely vertically below the pulley. If the tension in the string was 1.04 N, find the force exerted on the pulley.

  • A 0.52 N
  • B 2.08 N
  • C 2 6 √ 3 2 5 N
  • D 2 6 √ 2 2 5 N

Q7:

A body 𝐴 of mass 864 g rests on a smooth horizontal table. It is connected, by a light inextensible string passing over a smooth pulley fixed to the edge of the table, to a body 𝐡 of mass 470 g hanging freely vertically below the pulley. Body 𝐡 is attached by a similar string to another body 𝐢 of mass π‘š hanging freely vertically below it. Given that the force exerted on the axle of the pulley is 4 3 2 √ 2 g-wt, determine the tension 𝑇 in the string connecting bodies 𝐡 and 𝐢 , and find the value of π‘š . Take 𝑔 = 9 . 8 / m s 2 .

  • A 𝑇 = 6 2 9 g - , π‘š = 1 2 5 8 g
  • B 𝑇 = 2 3 5 g - , π‘š = 4 7 0 g
  • C 𝑇 = 8 6 4 g - , π‘š = 1 7 2 8 g
  • D 𝑇 = 1 9 7 g - , π‘š = 3 9 4 g

Q8:

A body 𝐴 of mass 258 g rests on a smooth horizontal table. It is connected by a light inextensible string passing over a smooth pulley, fixed to the edge of the table, to another body 𝐡 of mass 258 g hanging freely vertically below the pulley. The system was released from rest and, 4 seconds later, the string broke. Find the velocity of each of the two bodies 𝑣 𝐴 and 𝑣 𝐡 one second after the string broke. Take the acceleration due to gravity 𝑔 = 9 . 8 / m s 2 .

  • A 𝑣 = 1 9 . 6 / 𝐴 m s , 𝑣 = 2 4 . 5 / 𝐡 m s
  • B 𝑣 = 4 . 9 / 𝐴 m s , 𝑣 = 1 4 . 7 / 𝐡 m s
  • C 𝑣 = 4 . 9 / 𝐴 m s , 𝑣 = 9 . 8 / 𝐡 m s
  • D 𝑣 = 1 9 . 6 / 𝐴 m s , 𝑣 = 2 9 . 4 / 𝐡 m s

Q9:

A body 𝐴 of mass 737 g was resting on a smooth horizontal table and was connected by a light inextensible string passing over a smooth pulley, fixed at the edge of the table, to another body 𝐡 of mass 275 g which was hanging freely. The system was released from rest. Then 2.3 seconds later, the string snapped. Find the distance that body 𝐴 covered in the first 2 seconds after the string snapped. Take the acceleration due to gravity 𝑔 = 9 . 8 / m s 2 .

Q10:

A body 𝐴 of mass 382 g was placed on a smooth horizontal table. It was connected by a light inextensible string, passing over a smooth pulley fixed to the edge of the table, to another body 𝐡 of mass 382 g hanging vertically directly below the pulley. The system was released from rest and moved for 1.9 seconds before the string snapped. When the string snapped, body 𝐡 was 432 cm above the ground. Find the time it took for body 𝐡 to reach the ground after the sting snapped. Take the acceleration due to gravity 𝑔 = 9 . 8 / m s 2 .

  • A 3 2 3 3 4 4 s
  • B 2 4 1 7 0 6 s
  • C 4 3 2 9 3 1 s
  • D 2 7 7 0 s

Q11:

Two masses 𝐴 and 𝐡 of 231 and 393 grams, respectively, are connected to each other by a light inextensible string 𝑆 1 and placed on a smooth horizontal table. Mass 𝐴 is also connected, by another similar string 𝑆 2 which passes over a smooth pulley fixed at the edge of the table, to a body 𝐢 of mass 351 g hanging freely vertically below the pulley. Given that the system was released from rest, find the tensions 𝑇 1 and 𝑇 2 in the two strings 𝑆 1 and 𝑆 2 , respectively. Take the acceleration due to gravity 𝑔 = 9 . 8 / m s 2 .

  • A 𝑇 = 2 2 4 . 6 4 1 g - , 𝑇 = 1 4 7 . 8 4 2 g -
  • B 𝑇 = 3 9 3 1 g - , 𝑇 = 2 5 1 . 5 2 2 g -
  • C 𝑇 = 3 9 3 1 g - , 𝑇 = 8 3 . 1 6 2 g -
  • D 𝑇 = 1 4 1 . 4 8 1 g - , 𝑇 = 2 2 4 . 6 4 2 g -

Q12:

A body 𝐴 of mass 180 g is resting on a smooth horizontal table. It is connected by a light inelastic string which passes over a smooth pulley, fixed to the edge of the table, to another body 𝐡 of mass 120 g hanging freely vertically below the pulley. When body 𝐴 is 90 cm away from the pulley, the system is released from rest. Determine the speed at which body 𝐴 collides with the pulley. Take 𝑔 = 9 . 8 / m s 2 .

  • A 8 4 √ 5 cm/s
  • B 8 4 √ 1 5 cm/s
  • C 4 2 √ 1 0 5 cm/s
  • D 8 4 √ 1 0 cm/s

Q13:

A body of mass 7 kg was on a smooth horizontal table. It was attached by two light inextensible strings passing over two smooth pulleys fixed at opposite ends of the table to two bodies of masses π‘š 1 and π‘š 2 hanging freely below their respective pulleys. The body and the pulleys were on the same horizontal level. When the system was released from rest, the tension was 10.5 N in the first string and 39.9 N in the second. Determine the acceleration of the system π‘Ž and the masses π‘š 1 and π‘š 2 . Take 𝑔 = 9 . 8 / m s 2 .

  • A π‘Ž = 7 . 2 / m s 2 , π‘š = 0 . 6 1 8 1 k g , π‘š = 1 5 . 3 4 6 2 k g
  • B π‘Ž = 4 . 2 / m s 2 , π‘š = 0 . 7 5 1 k g , π‘š = 1 5 . 3 4 6 2 k g
  • C π‘Ž = 7 . 2 / m s 2 , π‘š = 0 . 6 1 8 1 k g , π‘š = 7 . 1 2 5 2 k g
  • D π‘Ž = 4 . 2 / m s 2 , π‘š = 0 . 7 5 1 k g , π‘š = 7 . 1 2 5 2 k g

Q14:

A body of mass 45 g rests on a smooth horizontal table. Two pulleys, 𝐴 and 𝐡 , are fixed at opposite ends of the table. The body is connected by two light inextensible strings passing over the pulleys, 𝐴 and 𝐡 , two bodies of masses 41 g and 12 g hanging freely vertically below their respective pulleys. The system was released from rest. Determine the tension in each string 𝑇 𝐴 and 𝑇 𝐡 in dynes. Take 𝑔 = 9 . 8 / m s 2 .

  • A 𝑇 = 1 1 8 9 0 𝐴 dynes, 𝑇 = 3 4 8 0 𝐡 dynes
  • B 𝑇 = 4 0 1 8 0 𝐴 dynes, 𝑇 = 1 1 7 6 0 𝐡 dynes
  • C 𝑇 = 4 0 0 6 1 . 1 𝐴 dynes, 𝑇 = 1 1 7 2 5 . 2 𝐡 dynes
  • D 𝑇 = 2 8 2 9 0 𝐴 dynes, 𝑇 = 1 5 2 4 0 𝐡 dynes
  • E 𝑇 = 4 0 2 9 8 . 9 𝐴 dynes, 𝑇 = 1 1 7 9 4 . 8 𝐡 dynes

Q15:

A body of mass 7 kg rests on a smooth horizontal table with two pulleys fixed at opposite ends. The body is connected by light inextensible strings passing over each of the two pulleys to two bodies, 𝐴 and 𝐡 , of masses 8 kg and 6 kg, respectively, hanging freely vertically below each of the pulleys. Before the system was released from rest, the bodies, 𝐴 and 𝐡 , were 6.3 m and 3.5 m above the ground, respectively. One second after the system was released, both of the strings were cut. Find the times 𝑑 𝐴 and 𝑑 𝐡 taken for each of the two bodies, 𝐴 and 𝐡 , to reach the ground. Take the acceleration due to gravity 𝑔 = 9 . 8 / m s 2 .

  • A 𝑑 = 2 3 4 4 𝐴 s , 𝑑 = 9 1 9 𝐡 s
  • B 𝑑 = 2 9 4 0 𝐴 s , 𝑑 = 2 4 3 5 𝐡 s
  • C 𝑑 = 1 𝐴 s , 𝑑 = 1 7 2 1 𝐡 s
  • D 𝑑 = 1 𝐴 s , 𝑑 = 1 𝐡 s

Q16:

A body of mass 428 g was placed on a smooth horizontal table with a pulley fixed at each end. A light inextensible string runs over one of the pulleys and connects the body on the table to a mass of 737 g hanging freely below the pulley. Similarly, a second light inextensible string runs over the other pulley and connects the body to a mass of 347 g hanging freely below that pulley. The two pulleys and the body on the table are in the same horizontal line. Given that the two masses started at the same height above the ground, find the vertical distance between them 0.6 seconds after the system was released from rest. Take 𝑔 = 9 . 8 / m s 2 .

Q17:

A box of mass 120 g was resting on a smooth horizontal table with a smooth pulley fixed at each end. A light inextensible string passed over one of the pulleys, 𝑃 𝐴 , and connected the box to body 𝐴 of mass 470 g which was hanging freely vertically below the pulley. Another similar string passed over pulley 𝑃 𝐡 and connected the box with body 𝐡 of mass 390 g hanging freely vertically below this pulley. When the box was 260 cm from pulley 𝑃 𝐴 , the system was released from rest. One second later, the mass of body 𝐴 was reduced by 80 g. Find the time 𝑑 taken from the moment the weight was reduced for the box to collide with pulley 𝑃 𝐴 . Take 𝑔 = 9 . 8 / m s 2 .

Q18:

A box of mass 33 g was resting on a smooth horizontal table with a smooth pulley fixed at each end. A light inextensible string passed over one of the pulleys, 𝑃 𝐴 , and connected the box to body 𝐴 of mass 26 g which was hanging freely vertically below the pulley. Another similar string passed over pulley 𝑃 𝐡 and connected the box with body 𝐡 of mass 24 g hanging freely vertically below this pulley. The system was released from rest. Find the force exerted on both of the pulleys, 𝑃 𝐴 and 𝑃 𝐡 , rounding your answer to the nearest two decimal places. Take 𝑔 = 9 . 8 / m s 2 .

  • A 𝑃 = 3 6 0 3 4 . 1 6 𝐴 d y n e s , 𝑃 = 3 3 2 6 2 . 3 0 𝐡 d y n e s
  • B 𝑃 = 4 9 7 3 2 . 0 5 𝐴 d y n e s , 𝑃 = 4 9 7 3 2 . 0 5 𝐡 d y n e s
  • C 𝑃 = 8 6 8 . 2 9 𝐴 d y n e s , 𝑃 = 8 0 1 . 5 0 𝐡 d y n e s
  • D 𝑃 = 3 5 1 6 5 . 8 7 𝐴 d y n e s , 𝑃 = 3 4 0 6 3 . 8 0 𝐡 d y n e s

Q19:

A body of mass 203 g rests on a rough horizontal table. It is connected by a light inextensible string, passing over a smooth pulley fixed to the edge of the table, to a body of mass 493 g hanging freely vertically below the pulley. Given that the coefficient of friction between the first body and the table is 0.2, find the acceleration of the system. Take 𝑔 = 9 . 8 / m s 2 .

Q20:

Body 𝐴 of mass 16 g rests on a rough horizontal table. It is connected, by a light inextensible string passing over a smooth pulley fixed to the edge of the table, to body 𝐡 of mass 48 g hanging freely vertically below the pulley. The system was released from rest. Given that the coefficient of friction between the table and body 𝐴 was 0.2, determine the distance covered by body 𝐴 in the first second of its motion. Take 𝑔 = 9 . 8 / m s 2 .

Q21:

A body of mass 165 g rests on a rough horizontal table 135 cm from the edge. It is connected, by a light inextensible string passing over a smooth pulley fixed to the edge of the table, to another body of the same mass hanging freely vertically below the pulley 96 cm above the ground. The system was released from rest. Given that the coefficient of friction between the table and the body is 1 6 , determine the velocity of the system when the hanging body reaches the ground. Take 𝑔 = 9 . 8 / m s 2 .

Q22:

A body of mass 200 g rests on a rough horizontal table. It is connected by a light inextensible string passing over a smooth pulley, fixed to the edge of the table, to another body of the same mass hanging freely below the pulley 2 cm above the ground. The coefficient of friction between the table and the body resting on it is 1 3 . Given that the system was released from rest, and the hanging body descended until it hit the ground, how much further did the body on the table travel until it came to rest? Take the acceleration due to gravity 𝑔 = 9 . 8 / m s 2 .

Q23:

A body weighing 10 g was placed on a rough horizontal table. It was connected to a light inextensible string which passed over a smooth pulley at the edge of the table. The other end of the string held a body of mass 40 g which was hanging vertically 245 cm above the ground. Given that the system was released from rest and that the coefficient of friction between the body and the table was 4 5 , find the horizontal distance covered by the body on the table after the hanging body reached the ground. Take 𝑔 = 9 . 8 / m s 2 .

Q24:

A body of mass 366 g rests on a smooth horizontal table. It is connected, by a light inextensible string passing over a smooth pulley fixed to the edge of the table, to another body of mass π‘š g hanging freely vertically below the pulley. Given that the tension in the string was 61 g-wt, determine the value of π‘š . Take the acceleration due to gravity 𝑔 = 9 . 8 / m s 2 .

Q25:

Two bodies of masses 120 kilograms and 142 kilograms are attached to the ends of a string passing over a smooth pulley fixed to the edge of a smooth table. The body of larger mass is placed on the table, while the smaller one is hanging vertically below the pulley such that the horizontal part of the string is perpendicular to the table’s edge. Determine the force exerted on the pulley, given that the gravitational acceleration 𝑔 = 9 . 8 / m s 2 .