An object of mass 10 kg is projected from ground with speed 40 m/s at an angle `60^(@)` with horizontal the rate of change of momentum of object one second after projection in SI unit is
[ Take g = 9.8 m/`s^(2)` ]

Options

A. 73
B. 98
C. 176
D. 140

Answer

To solve the problem, we need to determine the rate of change of momentum of the object one second after it has been projected. Here are the steps to find the solution:

### Step 1: Understand the Problem
We have an object of mass \( m = 10 \, \text{kg} \) projected with an initial speed of \( u = 40 \, \text{m/s} \) at an angle of \( 60^\circ \) with the horizontal. We need to find the rate of change of momentum one second after the projection.

### Step 2: Identify Forces Acting on the Object
After the object is projected, the only force acting on it is the gravitational force, which acts downward. The gravitational force can be calculated using the formula:
\[ F = m \cdot g \]
where \( g = 9.8 \, \text{m/s}^2 \).

### Step 3: Calculate the Gravitational Force
Substituting the values we have:
\[ F = 10 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 98 \, \text{N} \]

### Step 4: Relate Force to Rate of Change of Momentum
According to Newton's second law, the force acting on an object is equal to the rate of change of momentum:
\[ F = \frac{\Delta p}{\Delta t} \]
where \( \Delta p \) is the change in momentum and \( \Delta t \) is the change in time. Here, since we are looking for the rate of change of momentum at \( t = 1 \, \text{s} \), we can express this as:
\[ \frac{\Delta p}{\Delta t} = F \]

### Step 5: Conclusion
Since the only force acting on the object is the gravitational force, the rate of change of momentum one second after projection is equal to the gravitational force:
\[ \frac{\Delta p}{\Delta t} = 98 \, \text{N} \]

Thus, the rate of change of momentum of the object one second after projection is:
\[ \boxed{98 \, \text{kg m/s}^2} \]