JEE Advanced

1. A block of mass 1 kg is suspended from a spring of spring constant 100 N/m. The block is displaced from its equilibrium position and released. Find the maximum elongation of the spring.

Shortcut Method:

• The maximum elongation of the spring is given by: $$\Delta x=\sqrt{\frac{mg}{k}}=\sqrt{\frac{(1 \text{ kg})(9.81 \text{ m/s}^2)}{100 \text{ N/m}}}$$ $$\Delta x=0.316 \text{ m}$$

2. A body of mass 2 kg is attached to a light spring of spring constant 200 N/m. The body is pulled 10 cm from its equilibrium position and released. Find the maximum velocity of the body.

Shortcut Method:

• The maximum velocity of the body is given by: $$v_{max}=\omega A=\sqrt{\frac{k}{m}}A=\sqrt{\frac{200 \text{ N/m}}{2 \text{ kg}}}(0.1 \text{ m})$$ $$v_{max}=1 \text{ m/s}$$

3. A body of mass 1 kg is attached to a light spring of spring constant 100 N/m. The body is pulled 10 cm from its equilibrium position and released. Find the time period of oscillation.

Shortcut Method:

• The time period of oscillation is given by: $$T=2\pi\sqrt{\frac{m}{k}}=2\pi\sqrt{\frac{1 \text{ kg}}{100 \text{ N/m}}}$$ $$T=0.628 \text{ s}$$

4. A block of mass 2 kg is placed on a horizontal surface. A force of 10 N is applied to the block for 5 seconds. Find the work done by the force.

Shortcut Method:

• The work done by the force is given by: $$W=Fs=(10 \text{ N})(5 \text{ s})(2 \text{ m/s})$$ $$W=100 \text{ J}$$

5. A block of mass 2 kg is moving on a horizontal surface with a velocity of 5 m/s. The block collides with a spring of spring constant 200 N/m. Find the maximum compression of the spring.

Shortcut Method:

• The maximum compression of the spring is given by: $$\Delta x=\frac{1}{2}\frac{mv^2}{k}=\frac{1}{2}\frac{(2 \text{ kg})(5 \text{ m/s})^2}{200 \text{ N/m}}$$ $$\Delta x=0.25 \text{ m}$$

CBSE Board

1. A body of mass 1 kg is suspended from a spring of spring constant 100 N/m. The block is displaced from its equilibrium position and released. Find the maximum elongation of the spring.

Shortcut Method:

• The maximum elongation of the spring is given by: $$\Delta x=\sqrt{\frac{mg}{k}}=\sqrt{\frac{(1 \text{ kg})(9.81 \text{ m/s}^2)}{100 \text{ N/m}}}$$ $$\Delta x=0.316 \text{ m}$$

2. A body of mass 2 kg is attached to a light spring of spring constant 200 N/m. The body is pulled 10 cm from its equilibrium position and released. Find the maximum velocity of the body.

Shortcut Method:

• The maximum velocity of the body is given by: $$v_{max}=\omega A=\sqrt{\frac{k}{m}}A=\sqrt{\frac{200 \text{ N/m}}{2 \text{ kg}}}(0.1 \text{ m})$$ $$v_{max}=1 \text{ m/s}$$

3. A body of mass 1 kg is attached to a light spring of spring constant 100 N/m. The body is pulled 10 cm from its equilibrium position and released. Find the time period of oscillation.

Shortcut Method:

• The time period of oscillation is given by: $$T=2\pi\sqrt{\frac{m}{k}}=2\pi\sqrt{\frac{1 \text{ kg}}{100 \text{ N/m}}}$$ $$T=0.628 \text{ s}$$

4. A block of mass 2 kg is placed on a horizontal surface. A force of 10 N is applied to the block for 5 seconds. Find the work done by the force.

Shortcut Method:

• The work done by the force is given by: $$W=Fs=(10 \text{ N})(5 \text{ s})(1 \text{ m})$$ $$W=50 \text{ J}$$

5. A block of mass 2 kg is moving on a horizontal surface with a velocity of 5 m/s. The block collides with a spring of spring constant 200 N/m. Find the maximum compression of the spring.

Shortcut Method:

• The maximum compression of the spring is given by: $$\Delta x=\frac{1}{2}\frac{mv^2}{k}=\frac{1}{2}\frac{(2 \text{ kg})(5 \text{ m/s})^2}{200 \text{ N/m}}$$ $$\Delta x=0.25 \text{ m}$$