A small particle of mass m is projected at an angle θ with the x–axis with an initial velocity v₀ in the x–y plane as shown in the figure. At a time t<v_osin/g, the angular momentum of the particle is

$negative mgv subscript straight o space straight t squared space cos space straight theta space bold j with bold hat on top$
$mgv subscript 0 straight t space cos space straight theta space bold k with bold hat on top$
$negative 1 half space mgv subscript 0 straight t squared space cos space straight theta bold space bold k with bold hat on top bold space$
$1 half space mgv subscript straight o space straight t squared space cos space straight theta space bold i with bold hat on top$

Solution

negative 1 half space mgv subscript 0 straight t squared space cos space straight theta bold space bold k with bold hat on top bold space

The angular momentum of the projectile is given by,
L = m (r x v)
$straight L space equals space straight m space left square bracket space straight v subscript 0 space cos space straight theta space straight t space bold i with hat on top space plus space left parenthesis straight v subscript 0 space sin space straight theta space minus space gt right parenthesis bold j with hat on top right square bracket space space space space space space space space space space space space space straight x space left square bracket space straight v subscript straight o space cos space straight theta space straight t space bold i with hat on top space plus space left parenthesis straight v subscript 0 space sin space straight theta minus space gt right parenthesis bold j with hat on top right square bracket equals space mv subscript 0 space cos space θt space open square brackets negative 1 half gt close square brackets bold space bold k with bold hat on top bold space bold equals space minus 1 half space mgv subscript 0 space straight t squared space cos space straight theta bold space bold k with bold hat on top$

Some More Questions From Units and Measurement Chapter

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Units And Measurement

Some More Questions From Units and Measurement Chapter

Can we use same units for different physical quantities?

Can we use different units to measure same physical quantity?

To measure a physical quantity X, the unit U is repeatedly used for n times. What is the magnitude of physical quantity?

Does the numerical factor in the quantitative measurement depend on the system of unit used?

Is one unit sufficient to measure a physical quantity?

Can a physical quantity have two or more units? Give example.

What are fundamental quantities?

How many fundamental quantities are there in mechanics?

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Units And Measurement

A small particle of mass m is projected at an angle θ with the x–axis with an initial velocity v0 in the x–y plane as shown in the figure. At a time t<vosin/g, the angular momentum of the particle is

Some More Questions From Units and Measurement Chapter

Can we use same units for different physical quantities?

Can we use different units to measure same physical quantity?

To measure a physical quantity X, the unit U is repeatedly used for n times. What is the magnitude of physical quantity?

Does the numerical factor in the quantitative measurement depend on the system of unit used?

Is one unit sufficient to measure a physical quantity?

Can a physical quantity have two or more units? Give example.

What are fundamental quantities?

How many fundamental quantities are there in mechanics?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation