A 120 g mass has a velocity `vecv=2hati+5hatj m s^(-1)` at a certain instant. Its kinetic energy is

Options

A. 3 J
B. 4 J
C. 5 J
D. 1.74 J

Explanation

To find the kinetic energy of the mass, we can follow these steps:

### Step 1: Convert the mass from grams to kilograms
The mass given is 120 g. To convert grams to kilograms, we use the conversion factor \(1 \text{ kg} = 1000 \text{ g}\).

\[ m = \frac{120 \text{ g}}{1000} = 0.12 \text{ kg} \]

### Step 2: Determine the velocity vector
The velocity vector is given as:

\[ \vec{v} = 2\hat{i} + 5\hat{j} \text{ m/s} \]

### Step 3: Calculate the magnitude of the velocity
The magnitude of the velocity vector can be calculated using the formula:

\[ |\vec{v}| = \sqrt{(v_x)^2 + (v_y)^2} \]

where \(v_x = 2\) m/s and \(v_y = 5\) m/s.

\[ |\vec{v}| = \sqrt{(2)^2 + (5)^2} = \sqrt{4 + 25} = \sqrt{29} \text{ m/s} \]

### Step 4: Use the kinetic energy formula
The kinetic energy (KE) can be calculated using the formula:

\[ KE = \frac{1}{2} m v^2 \]

### Step 5: Substitute the values into the kinetic energy formula
Now, substitute the mass and the square of the magnitude of the velocity into the kinetic energy formula:

\[ KE = \frac{1}{2} \times 0.12 \text{ kg} \times (\sqrt{29})^2 \]

Since \((\sqrt{29})^2 = 29\):

\[ KE = \frac{1}{2} \times 0.12 \text{ kg} \times 29 \]

### Step 6: Calculate the kinetic energy
Now, calculate the value:

\[ KE = 0.06 \times 29 = 1.74 \text{ J} \]

### Final Answer
The kinetic energy of the mass is:

\[ KE = 1.74 \text{ J} \]

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