Question

The angular momentum of a body is given by L = (4t² + 2t + 7) kg m² s1. The net torque acting on the body at t = 2 sis 18 Nm 10 Nm 16 Nm 8 Nm​

Answer 1

Answer:

The correct option is C

24

^

k

Nm

As we know,

→

τ

net

=

d

→

L

sys

d

t

Given:

→

L

=

(

4

t

2

+

6

)

^

k

d

→

L

d

t

=

8

t

^

k

∴

At

t

=

3

sec

d

→

L

d

t

=

(

8

×

3

)

^

k

=

24

^

k

Nm

∴

Option (c) is correct.

Answer 2

Answer:

The angular momentum of a body is given by L = (4t² + 2t + 7) kg m² /s. The net torque acting on the body at t = 2 is $18\ Nm$

Explanation:

• The rate of change of angular momentum of a body with respect to time can be defined as the torque acting on that body.

• Let L be the angular momentum, t be the time and τ be the torque.

      τ is given by the expression,

      τ = $\frac{dL}{dt}$   ...(1)

• In the question, it is given that,

      $L = (4t^{2} +2t+7) kgm^{2}/ s$

      Taking the derivative of L with respect to time,

      τ = $\frac{dL}{dt} = 8t+2$  ...(2)

      From the question, $t = 2s$

     Substitute the value of t into equation (2)

     τ = $\frac{dL}{dt} = (8\times 2)+2 = 18 Nm$

• Answer is $18\ Nm$