A homogeneous plate P Q R S T is as shown in figure. The centre of mass of plate lies at midpoint A of segment Q T. Then the ratio of (b/a) is (P Q=P T=b ; Q R=R S=S T=a)

Question

A homogeneous plate P Q R S T is as shown in figure. The centre of mass of plate lies at midpoint A of segment Q T. Then the ratio of (b/a) is (P Q=P T=b ; Q R=R S=S T=a) (A) (13/4) (B) (13/2) (C) √(13/2) (D) √(13/4)

Tardigrade Admin · Accepted Answer

If centre of mass is at A a2 σ (a/2)=σ (1/2) a b sin θ (1/3) b sin θ <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/9c5778eb890b2c2b784bf0a771133420-.png" /> or (b/a)=√(13/4)

Q. A homogeneous plate $PQRST$ is as shown in figure. The centre of mass of plate lies at midpoint $A$ of segment $QT$ . Then the ratio of $\frac{b}{a}$ is $(PQ = PT = b; QR = RS = ST = a)$

$\frac{13}{4}$

$\frac{13}{2}$

$\frac{13}{2}$

$\frac{13}{4}$

If centre of mass is at $A$
$a^{2} σ \frac{a}{2} = σ \frac{1}{2} ab sin θ \frac{1}{3} b sin θ$

or $\frac{b}{a} = \frac{13}{4}$

Q. A homogeneous plate PQRST is as shown in figure. The centre of mass of plate lies at midpoint A of segment QT. Then the ratio of ab​ is (PQ=PT=b;QR=RS=ST=a)

413​

213​

213​​

413​​

If centre of mass is at A a2σ2a​=σ21​absinθ31​bsinθ or ab​=413​​

Q. A homogeneous plate $PQRST$ is as shown in figure. The centre of mass of plate lies at midpoint $A$ of segment $QT$ . Then the ratio of $\frac{b}{a}$ is $(PQ = PT = b; QR = RS = ST = a)$

$\frac{13}{4}$

$\frac{13}{2}$

$\frac{13}{2}$

$\frac{13}{4}$

If centre of mass is at $A$
$a^{2} σ \frac{a}{2} = σ \frac{1}{2} ab sin θ \frac{1}{3} b sin θ$

or $\frac{b}{a} = \frac{13}{4}$