141482 A bullet enters in a piece of wood with velocity \(v_{0}\) and the resistive force acting on the bullet in the wood is proportional to \(v^{\frac{1}{3}}\). If the total distance travelled by the bullet is proportional to \(\left(v_{0}\right)^{\beta}\), then the value of \(\beta\) is

141485 As shown in the figure, two particle each of mass \(m\) tied at the ends of a light string of length \(2 a\) are kept on a frictionless horizontal surface. When the mid-point \((P)\) of the string is pulled vertically upwards with a small but constant force \(F\), the particles move towards each other on the surface. Magnitude of acceleration each particle, when the separation between them becomes \(2 \mathrm{x}\) is

141486 A body is projected horizontally from the top of a tower of height \(180 \mathrm{~m}\) with a velocity of 20 \(\mathrm{ms}^{-1}\). If acceleration due to gravity is \(10 \mathrm{~ms}^{-2}\), then match the following.
| | List-I | | List-II |
| :--- | :--- | :--- | :--- |
| A | Velocity of the body after 1 second \lt br> $\left(\mathrm{ms}^{-1}\right.$ ) | I | 5 |
| B | Horizontal displacement of the \lt br> body after 1 second (in metres) | II | 20 |
| C | Vertical displacement of the body \lt br> after 1 second (in metres) | III | 10 |
| D | Vertical velocity of the body after 1 \lt br> second (in $\mathrm{ms}^{-1}$ ) | IV | 22.4 |

141487 A solid ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at the speed \(60 \mathrm{cms}^{-1}\) on the string, when the car is at rest. When the car accelerates on a horizontal road, then speed of the pulse is \(66 \mathrm{cms}^{-1}\). The acceleration of the car is nearly \(\left(\mathrm{g}=10 \mathrm{~ms}^{-\mathbf{2}}\right)\)

141482 A bullet enters in a piece of wood with velocity \(v_{0}\) and the resistive force acting on the bullet in the wood is proportional to \(v^{\frac{1}{3}}\). If the total distance travelled by the bullet is proportional to \(\left(v_{0}\right)^{\beta}\), then the value of \(\beta\) is

141485 As shown in the figure, two particle each of mass \(m\) tied at the ends of a light string of length \(2 a\) are kept on a frictionless horizontal surface. When the mid-point \((P)\) of the string is pulled vertically upwards with a small but constant force \(F\), the particles move towards each other on the surface. Magnitude of acceleration each particle, when the separation between them becomes \(2 \mathrm{x}\) is

141486 A body is projected horizontally from the top of a tower of height \(180 \mathrm{~m}\) with a velocity of 20 \(\mathrm{ms}^{-1}\). If acceleration due to gravity is \(10 \mathrm{~ms}^{-2}\), then match the following.
| | List-I | | List-II |
| :--- | :--- | :--- | :--- |
| A | Velocity of the body after 1 second \lt br> $\left(\mathrm{ms}^{-1}\right.$ ) | I | 5 |
| B | Horizontal displacement of the \lt br> body after 1 second (in metres) | II | 20 |
| C | Vertical displacement of the body \lt br> after 1 second (in metres) | III | 10 |
| D | Vertical velocity of the body after 1 \lt br> second (in $\mathrm{ms}^{-1}$ ) | IV | 22.4 |

141487 A solid ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at the speed \(60 \mathrm{cms}^{-1}\) on the string, when the car is at rest. When the car accelerates on a horizontal road, then speed of the pulse is \(66 \mathrm{cms}^{-1}\). The acceleration of the car is nearly \(\left(\mathrm{g}=10 \mathrm{~ms}^{-\mathbf{2}}\right)\)

141482 A bullet enters in a piece of wood with velocity \(v_{0}\) and the resistive force acting on the bullet in the wood is proportional to \(v^{\frac{1}{3}}\). If the total distance travelled by the bullet is proportional to \(\left(v_{0}\right)^{\beta}\), then the value of \(\beta\) is

141485 As shown in the figure, two particle each of mass \(m\) tied at the ends of a light string of length \(2 a\) are kept on a frictionless horizontal surface. When the mid-point \((P)\) of the string is pulled vertically upwards with a small but constant force \(F\), the particles move towards each other on the surface. Magnitude of acceleration each particle, when the separation between them becomes \(2 \mathrm{x}\) is

141486 A body is projected horizontally from the top of a tower of height \(180 \mathrm{~m}\) with a velocity of 20 \(\mathrm{ms}^{-1}\). If acceleration due to gravity is \(10 \mathrm{~ms}^{-2}\), then match the following.
| | List-I | | List-II |
| :--- | :--- | :--- | :--- |
| A | Velocity of the body after 1 second \lt br> $\left(\mathrm{ms}^{-1}\right.$ ) | I | 5 |
| B | Horizontal displacement of the \lt br> body after 1 second (in metres) | II | 20 |
| C | Vertical displacement of the body \lt br> after 1 second (in metres) | III | 10 |
| D | Vertical velocity of the body after 1 \lt br> second (in $\mathrm{ms}^{-1}$ ) | IV | 22.4 |

141487 A solid ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at the speed \(60 \mathrm{cms}^{-1}\) on the string, when the car is at rest. When the car accelerates on a horizontal road, then speed of the pulse is \(66 \mathrm{cms}^{-1}\). The acceleration of the car is nearly \(\left(\mathrm{g}=10 \mathrm{~ms}^{-\mathbf{2}}\right)\)

141482 A bullet enters in a piece of wood with velocity \(v_{0}\) and the resistive force acting on the bullet in the wood is proportional to \(v^{\frac{1}{3}}\). If the total distance travelled by the bullet is proportional to \(\left(v_{0}\right)^{\beta}\), then the value of \(\beta\) is

141485 As shown in the figure, two particle each of mass \(m\) tied at the ends of a light string of length \(2 a\) are kept on a frictionless horizontal surface. When the mid-point \((P)\) of the string is pulled vertically upwards with a small but constant force \(F\), the particles move towards each other on the surface. Magnitude of acceleration each particle, when the separation between them becomes \(2 \mathrm{x}\) is

141486 A body is projected horizontally from the top of a tower of height \(180 \mathrm{~m}\) with a velocity of 20 \(\mathrm{ms}^{-1}\). If acceleration due to gravity is \(10 \mathrm{~ms}^{-2}\), then match the following.
| | List-I | | List-II |
| :--- | :--- | :--- | :--- |
| A | Velocity of the body after 1 second \lt br> $\left(\mathrm{ms}^{-1}\right.$ ) | I | 5 |
| B | Horizontal displacement of the \lt br> body after 1 second (in metres) | II | 20 |
| C | Vertical displacement of the body \lt br> after 1 second (in metres) | III | 10 |
| D | Vertical velocity of the body after 1 \lt br> second (in $\mathrm{ms}^{-1}$ ) | IV | 22.4 |

141487 A solid ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at the speed \(60 \mathrm{cms}^{-1}\) on the string, when the car is at rest. When the car accelerates on a horizontal road, then speed of the pulse is \(66 \mathrm{cms}^{-1}\). The acceleration of the car is nearly \(\left(\mathrm{g}=10 \mathrm{~ms}^{-\mathbf{2}}\right)\)